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['The diagram consists of two triangles, ABC and ACD, sharing the common side AC. Point D lies on the line segment AB.'] then, please answer, In the given figure, line AB is parallel to line CD, and their intersection is point O. If angle A is 25 degrees and angle D is 45 degrees, what is the measure of angle AOB? | <answer> 110° </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. These lines are parallel to each other. A transversal line, labeled as line l, intersects both lines a and b at points 1 and 2 respectively.'] then, please answer, In the given diagram, lines a and b are intersected by line l, where a is parallel to b. If angle 1 measures 60°, what is the degree measure of angle 2? | <answer> 120° </answer> |
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['The diagram shows a rectangular prism with two triangular faces. One of the triangular faces is labeled as angle 1, and the other is labeled as angle 2. The rectangular prism has three dimensions: length, width, and height. The triangular faces are formed by the edges of the prism that meet at the corners.'] then, please answer, If a rectangular piece of paper is folded according to the provided diagram, and angle 1 measures 40 degrees, what is the measure of angle 2? | <answer> 70° </answer> |
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['The diagram consists of two triangles, ABC and ADE, sharing the vertex A. Triangle ABC is an acute triangle with angles 60° at vertex B and 45° at vertex C. Triangle ADE is also an acute triangle with angle D equal to 45°. The line segment DE is parallel to BC.'] then, please answer, What is the measure of angle 1 when the set square is stacked as shown in the figure? | <answer> 105° </answer> |
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['The diagram consists of a rectangle labeled ABCD. Point C is connected to points A and B, forming two right angles at points A and B. The line segment AC is perpendicular to the line segment BC.'] then, please answer, What is the degree measure of angle ACB if angle CAB is 40 degrees and a rectangular piece of paper is folded into the shape depicted in the figure? | <answer> 70° </answer> |
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['The diagram consists of two parallel lines, labeled as line 1 and line 2. A transversal intersects both lines at points A and B, forming several angles. Angle 1 is adjacent to angle 2, and angle 3 is adjacent to angle 4. Additionally, angle 5 is formed by the intersection of the transversal with line 1.'] then, please answer, If a rectangular piece of paper is folded as depicted in the figure and angle 2 measures 50 degrees, what is the measure of angle 1? | <answer> 80° </answer> |
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['The diagram consists of two triangles, ABC and ABD, sharing the side AB. Triangle ABC is an equilateral triangle, while triangle ABD is a right triangle. The vertices of the triangles are labeled as A, B, C, and D.'] then, please answer, In the given illustration, Xiao Qiang positions the two vertices of a right-angled triangle board with a 30° angle on the opposite sides of a ruler, and measures angle 1 to be 55°. What is the degree measurement of angle 2? | <answer> 25° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line AC at point C. Angle 1 is formed between line AC and line AB, while angle 2 is formed between line AC and line CD.'] then, please answer, As shown in the diagram, a beam of light is shining on the ground at an angle of 60° with the horizontal plane. Now, a plane mirror CD is placed on the ground AB, so that the beam of light passes through the mirror and reflects to become a horizontal beam (angle 1=angle 2). The degree of angle angle DCA formed between the plane mirror CD and the ground AB is equal to (). | <answer> 30° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line CE at point C. Point E is located on the extension of line CE beyond point C.'] then, please answer, In the given illustration of triangle ABC, where angle ACB measures 90 degrees and angle B measures 60 degrees, with CD being parallel to AB, what is the measure of angle 1? | <answer> 30° </answer> |
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['The diagram shows two parallel lines, AB and CD, intersected by a transversal line, EF. The angles formed at the intersection points are labeled as ∠1, ∠2, ∠3, and ∠4. Angle α is formed between the transversal line EF and one of the parallel lines, either AB or CD.'] then, please answer, In the given illustration, a configuration of triangular boards is set up where the oblique sides of the two boards are parallel. The right-angle vertices of each board coincide with the oblique sides of the other. If angle C is 45°, what is the degree measure of angle α in the illustration? | <answer> 75° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point E is located on line CD, and point F is located on line AB. Line EF intersects line AD at point A.'] then, please answer, In the given figure, a ruler is placed alongside a triangle ABC, where angle A measures 30 degrees and angle B measures 60 degrees. The ruler intersects the two right angles of the triangle at points D and E, and the other side intersects the two right angles of the triangle at points F and A. What is the measure of angle CFA if angle CED measures 50 degrees? | <answer> 40° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line BD at point B. Point C lies on line AB, while point D lies on line CD.'] then, please answer, In the given illustration, it is shown that line AB is parallel to line CD, and line BC bisects angle ABD. If the measure of angle 1 is 65 degrees, what is the degree measure of angle 2? | <answer> 50° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line segment EF at points E and F. Point G is located on line segment EF. Additionally, there is a circle with center G that intersects line segment EF at point H.'] then, please answer, As shown in the figure, when the vertex of a right-angled triangle is placed on one side of a ruler, if angle 1 = 55°, the degree of angle 2 is () | <answer> 35° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point E is located on line AB, and point F is located on line CD. Line EF intersects line AG at point G and line FD at point F.'] then, please answer, In the given illustration, it is indicated that line AB is parallel to line CD. Line EF intersects AB and CD at points E and F respectively, and line EG bisects angle AEF. If angle 1 measures 35 degrees, what is the degree measurement of angle 2? | <answer> 70° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point E is located on line CD, and point F is located on line AB. Line EF intersects line CD at point D.'] then, please answer, In the given diagram, point D lies in the interior of angle EAB, with CD being parallel to AB and DF parallel to AE. Line segment DH is perpendicular to AB and intersects AB at point H. If angle A measures 40°, what is the measure of angle FDH? | <answer> 130° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line AE at point E. Point F is the intersection of line AF and line DE.'] then, please answer, In the given diagram, a regular ruler intersects with a right angle triangle ruler at points D and E, while the other side of the regular ruler passes through point A and intersects with the right angle side BC of the triangle ruler at point F. If the measure of angle CAF is 42°, what is the degree measure of angle CDE? | <answer> 48° </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. Point A is located on line a, while point B is located on line b. Point C is the intersection of line AC and line b. Angle 1 is formed between line AC and line b.'] then, please answer, As shown in the figure, aparallel b, ACperpendicular b, the foot is C, angle A＝40°, then angle 1 is equal to (). | <answer> 50° </answer> |
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['The diagram consists of two parallel lines, l1 and l2, intersected by line h at points A and B respectively. Line h is also intersected by line l3 at point C. The angles formed by the intersection of these lines are labeled as angle 1, angle 2, angle 3, and angle 4.'] then, please answer, Given that line l1 is parallel to line l2, and line l3 intersects l1 at point A and intersects l2 at point B, with the line l4 passing through point B and intersecting l1 at point C, if angle 3 is 50° and the sum of angles 1, 2, and 3 is 240°, what is the measure of angle 4? | <answer> 70° </answer> |
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['The diagram consists of two parallel lines, DE and BC. Point A is located on line DE, and point B is located on line BC.'] then, please answer, In the given triangle ABC, angle B measures 50° and angle C measures 70°. Line DE intersects at point A, and angle DAB measures 50°. What is the measure of angle EAC? | <answer> 70° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line DE at points B and D respectively.'] then, please answer, In the given diagram, if AB is parallel to CD and angle B measures 75 degrees while angle D measures 35 degrees, what is the measure of angle E? | <answer> 40° </answer> |
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['The diagram shows two parallel lines, labeled as line a and line b. There is an angle labeled as 1 on line a, and another angle labeled as 2 on line b. The angles 1 and 2 are adjacent and form a straight line.'] then, please answer, In the given diagram, line a is parallel to line b and angle 1 measures 60°. What is the measure of angle 2? | <answer> 120° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line EF at points E and F. Point E lies on line EF, which is perpendicular to both AB and CD.'] then, please answer, As shown in the diagram, AB is parallel to CD. EF is perpendicular to CD at point F. If angle BEF = 150°, then angle ABE = (). | <answer> 60° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the extension of side BC. Point E is the midpoint of segment AD. Point F is the intersection of line EF and side AB.'] then, please answer, Triangle ABC is depicted in the figure, where point D lies on the extension of side BC and point E is an arbitrary point on side AC. Line EF is drawn parallel to side BC, intersecting side AB at point F. Given that angle ACD measures 50 degrees and angle BAC measures 15 degrees, what is the measure of angle AFE? | <answer> 35° </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. Point A is located on line a, and point B is located on line b. There is a circle inscribed within the triangle formed by points A, B, and C. Angle 1 is an exterior angle of the triangle, while angle 2 is an interior angle of the triangle.'] then, please answer, Place a right-angled triangle ruler ABC with an angle of 30° as shown in the figure. Point A and C are located on lines a and b respectively. If a is parallel to b, and angle 1 = 40°, then the degree of angle 2 is (). | <answer> 20° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line EF at points E and F. Point M is the intersection of lines CM and EF.'] then, please answer, In the given diagram, it is shown that AB is parallel to CD, EF is perpendicular to AB at point E, and EF intersects CD at point F, while EM intersects CD at point M. If angle 1 measures 55 degrees, what is the measure of angle 2? | <answer> 35° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by a transversal line, EF. Point G is the intersection of EF and CD. Angle 1 is formed between EF and AB, while angle 2 is formed between EF and CD.'] then, please answer, If the measure of angle 1 is 47 degrees, what is the degree measure of angle 2? | <answer> 137° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line EF at points E and F. Point A is connected to point B, while point C is connected to point D.'] then, please answer, In the provided diagram, line AB is parallel to line CD. Points E and F are located on the side AC. If angle CED measures 70 degrees and angle BFC measures 130 degrees, what is the combined measurement of angle B and angle D? | <answer> 60° </answer> |
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['The diagram consists of two parallel lines, labeled as line AB and line CD. Point A is located on line AB, while point C is located on line CD. There is an angle labeled as 2x at the intersection of line AC and line AB. Additionally, there is another angle labeled as x at the intersection of line AC and line CD.'] then, please answer, If angle A measures 30° and angle 1 measures 40°, what is the measurement of angle 2 when the right angle vertex of a protractor is placed on one of the two parallel lines as shown in the figure? | <answer> 20° </answer> |
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['The diagram consists of three lines labeled as AB, AC, and BC. Point D is located on line AD, and point E is located on line AE. Additionally, there is a line segment DE that connects points D and E.'] then, please answer, In the given figure, point D is the intersection of the perpendicular bisectors of AB and AC in triangle ABC, while point E is the intersection of the perpendicular bisectors of AB and AC in the same triangle. If the measure of angle BAC is 110 degrees, what is the measure of angle DAE? | <answer> 40 </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. Point C lies on line b, and point A is connected to points B and C. Angle 1 is formed by the intersection of line BC and line AC. Angle 2 is formed by the intersection of line AB and line AC.'] then, please answer, In the given diagram, it's depicted that line a is parallel to line b, and the right-angled vertex C of right triangle ABC is situated on line b. If the measure of angle 1 is 20 degrees, what is the measure of angle 2? | <answer> 70 </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line CE at point C. Point E lies on line CE, and line EF is perpendicular to line CE.'] then, please answer, If AB is parallel to both CD and EF, and angle ABC is 130 degrees while angle BCE is 55 degrees, what is the measure of angle CEF? | <answer> 105° </answer> |
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['The diagram shows a triangle ABC with vertices A, B, and C. Point D is located on the line segment AB such that angle ADC is 18 degrees. The line segment BC is parallel to the line segment m.'] then, please answer, As shown in the diagram, line l is parallel to line m. The vertex B of equilateral triangle ABC lies on line m. The acute angle between side BC and line m is 18°. The degree measurement of angle α is () | <answer> 42° </answer> |
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['The diagram shows a triangle ABC with vertices A, B, and C. Point D is located on the side AB of the triangle.'] then, please answer, As shown in the diagram, in triangle ABC, angle A = 60°, AD = DC = DB, then the degree of angle B is (). | <answer> 30° </answer> |
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['The diagram shows a triangle ABC with vertices A, B, and C. Point D is located on side AB, and point E is located on side AC. The line segment DE is parallel to side BC.'] then, please answer, In the given triangle ABC, if the measure of angle B is 40°, and the perpendicular bisector of side AC intersects AC at point D and BC at point E, with the angle EAB to CAE ratio being 3, what is the measure of angle C? | <answer> 28° </answer> |
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['The diagram shows a triangle ABC with vertices A, B, and C. Point P is located inside the triangle.'] then, please answer, As shown in the diagram, in triangle ABC, AB = AC. Point P is a point inside triangle ABC, and angle PBC = angle PCA. If angle BPC = 115°, then the degree measure of angle A is (). | <answer> 50° </answer> |
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['The diagram shows a triangle ABC with vertices A, B, and C. Point P is located inside the triangle.'] then, please answer, In triangle ABC, AB = AC, angle B = 50°. P is a moving point on side AB (not coinciding with vertex A). The possible value of angle BPC could be (). | <answer> 80° </answer> |
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['The diagram shows two parallel lines, labeled as line a and line b, intersected by a transversal line labeled as line c. The intersection points of the transversal line with the parallel lines form several angles.'] then, please answer, In the given diagram, lines a and b pass through the vertices A and C of equilateral triangle ABC, and line b is parallel to line a. If angle 1 measures 42 degrees, what is the degree measure of angle 2? | <answer> 102° </answer> |
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['The diagram consists of a triangle ABC, where points A, B, and C are the vertices of the triangle. Point D lies on the line segment BC, dividing it into two segments, BD and DC.'] then, please answer, In the given triangle ABC, if AB is equal to AC and D is located on the perpendicular bisector of AB, with angle ADC measuring 80 degrees, what is the measure of angle C? | <answer> 40° </answer> |
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['The diagram shows a right-angled triangle ABC, where angle BAC is 90 degrees. Point D is located on the extension of side BC, and point E is located on the extension of side AB. The line segments AD and CE intersect at point F.'] then, please answer, What is the total perimeter of the five small rectangles in the given figure if the dimensions of the rectangle ABCD are AB = 6.0 and BC = 8.0? | <answer> 28 </answer> |
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['The diagram shows a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral. The sides AB, BC, CD, and DA connect these vertices in sequence. Additionally, there is a diagonal AC that connects points A and C.'] then, please answer, As shown in the diagram, angle DAB = 90°, angle DBA = 30°, AB = BC = √3, DC = √7. Then angle ACB = () | <answer> 30° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the side AC, and point E is located on the side AB. Line segments AD and BE intersect at point F.'] then, please answer, In the given diagram of triangle ABC, where AC is equal to BC, point D lies on side AC, and point E is located on the extension of CB. If angle C measures 50° and angle E measures 25°, what is the measure of angle BFE? | <answer> 40° </answer> |
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['The diagram consists of a triangle ABC, where point A is connected to points B and C. Point D lies on the line segment BC.'] then, please answer, Given the diagram of triangle ABC with angle B measuring 36 degrees and AB being equal to AC, and AD serving as the median of the triangle, what is the measure of angle BAD? | <answer> 54° </answer> |
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['The diagram consists of two parallel lines, m and n. Point A is located on line m, while point B is located on line n. Point C is the intersection of line AC and line BC. Angle 1 is formed between line AC and line m, while angle 2 is formed between line BC and line n.'] then, please answer, In the given diagram, line m is parallel to line n, and the vertex B of equilateral triangle ABC lies on line n. If angle 1 is 25 degrees, what is the measure of angle 2? | <answer> 35° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the line segment AB, point E is located on the line segment BC, and point F is located on the line segment AC. Additionally, there is a line segment DG that connects points D and G, and another line segment EG that connects points E and G.'] then, please answer, In the given diagram, if the perpendicular bisector of side AB intersects AB and BC at points D and E, and the perpendicular bisector of side AC intersects AC and BC at points F and G in triangle ABC, and angle BAC measures 100 degrees, what is the measure of angle EAG? | <answer> 20° </answer> |
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['The diagram consists of a triangle ABC, where points A, B, and C are the vertices of the triangle. Point D is located on the line segment AB.'] then, please answer, In the given diagram of triangle ABC, where AB is congruent to AC and angle A measures 40 degrees, if BD is the angle bisector of angle ABC and intersects AC at point D, what is the measure of angle CDB? | <answer> 75° </answer> |
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['The diagram consists of two triangles, ABC and APMN, sharing the vertex A. Point P lies on side BC of triangle ABC, and point Q lies on side AC of triangle ABC. The line segment AP is perpendicular to side BC, while the line segment AQ is perpendicular to side AC.'] then, please answer, In the given diagram of triangle ABC, if PM and QN are the perpendicular bisectors of line segments AB and AC respectively, and angle BAC measures 110 degrees, what is the measure of angle PAQ? | <answer> 40° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the side BC of the triangle. Point E is the midpoint of segment AD. Point F is the intersection point of line EF and line AC.'] then, please answer, As shown in the figure, triangle ABC is an equilateral triangle, AD is the median on side BC, point E is on AD, and DE = 0.5×BC. Then, angle AFE = (). | <answer> 105° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point E is the midpoint of side BC. Points G and H are located on sides AB and AC respectively. The line segments AG and AH intersect at point F.'] then, please answer, In the given diagram, triangle ABC is depicted, and the perpendicular bisectors of AB and AC intersect BC at points E and F respectively. What is the measure of angle EAF if angle BAC is 102 degrees? | <answer> 24° </answer> |
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["I'm sorry, but I cannot generate a description of the geometric diagram as you haven't provided one. Could you please provide me with more information or the diagram itself?"] then, please answer, What is the measure of angle CAD if AD equally divides angle BAC and AB is parallel to CD, and angle CDA is 70 degrees? | <answer> 70° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the line segment BC. Line AD intersects line L at point E.'] then, please answer, In the given diagram, if triangle ABC is depicted with AB equal to AC and the perpendicular bisector of AC intersecting BC at point D, and angle BAD measures 78 degrees, then what is the degree measure of angle B? | <answer> 34° </answer> |
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['The diagram consists of a triangle ABC, where points A, B, and C are the vertices of the triangle. Point P is located on side BC, and point M is located on side AB. Additionally, there is a line segment MN that passes through point P and intersects side AC at point N.'] then, please answer, What is the measure of angle APC in triangle ABC, where angle B equals 50 degrees and point P is located inside the triangle with the line MN passing through P intersecting AB and BC at points M and N? | <answer> 115° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the line segment BC, and point E is located on the line segment AD. The length of side AB is 10 units, and the length of side AC is 8 units.'] then, please answer, In the given diagram, if AD is the median of the equilateral triangle ABC and point E lies on AC with AE equal to AD, what is the measure of angle EDC? | <answer> 15° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the side BC of the triangle.'] then, please answer, Given a triangle ABC where AB = AD = CD, and angle C measures 38.5 degrees, what is the measure of angle BAD? | <answer> 26° </answer> |
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['The diagram consists of a right triangle ABC with vertices A, B, and C. Point T is located on the hypotenuse AC. The line segment AT intersects the circle centered at point A with radius AB at point T.'] then, please answer, In the given diagram, triangle ABC is a right triangle with angle CAB equal to 90 degrees and angle C equal to 48 degrees. If an arc is drawn with point B as the center and BA as the radius, intersecting CB at point T, and then connecting AT, what is the measure of angle CAT? | <answer> 21° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line BE at point D. Point E lies on the extension of line BC.'] then, please answer, In the given figure, if angle ABC measures 40 degrees and BD bisects angle ABC, and DE is parallel to AB passing through D and intersecting BC at point E, then what is the degree measure of angle DFB if point F lies on AB and satisfies DF = DE? | <answer> 40° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point A is connected to points B and C, forming a triangle ABC. Point E lies on the extension of line AB beyond point B.'] then, please answer, What is the measure of angle DAE if triangle ABC has AB equal to AC, angle B measures 65 degrees, and point D lies on the extension of BA, while AE bisects angle DAC? | <answer> 65° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the line segment AB, and point E is located on the line segment AC. The line segments DE and MN are parallel to each other.'] then, please answer, In the given illustration, if in the isosceles triangle ABC, AB is equal to AC and angle A measures 50°, and line MN is perpendicular to and bisects side AC at points D and E, then what is the measure of angle BCD? | <answer> 15° </answer> |
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['The diagram consists of a triangle ABC, where points A, B, and C are the vertices of the triangle. Point P is located on the side BC of the triangle.'] then, please answer, If in triangle ABC, angle ABC is equal to angle ACB and angle A measures 50 degrees, and P is a point inside the triangle with angle PBC equal to angle PCA, what is the measure of angle BPC? | <answer> 115° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is the midpoint of side BC. Point E lies on side AC such that DE is perpendicular to AC. The length of side AB is 10 units.'] then, please answer, In the given illustration, AD is the median of the equilateral triangle ABC. When a point E is selected on side AC such that AE is equal to AD, what is the measure of angle EDC? | <answer> 15° </answer> |
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['The diagram consists of a triangle ABC, where points A, B, and C are the vertices of the triangle. Point D is located on side BC such that AD is perpendicular to BC.'] then, please answer, In triangle ABC, where AB is equal to AC and AD is the median of side BC, and angle B measures 25°, what is the size of angle CAD? | <answer> 65° </answer> |
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['The diagram consists of a triangle ABC, where points A, B, and C are the vertices of the triangle. Point D lies on the line segment BC.'] then, please answer, In the given triangle ABC, if point D lies on the perpendicular bisector of AB and angle CAD measures 80 degrees while angle C measures 50 degrees, what is the measure of angle B? | <answer> 25° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the side BC of the triangle. Point E is the midpoint of the line segment AD. The line segment BE intersects the line segment AC at point F.'] then, please answer, In the given diagram of triangle ABC, where AB is equal to AC and angle A measures 40 degrees, if DE is the perpendicular bisector of AB, what is the degree measure of angle DBC? | <answer> 30° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the line segment BC.'] then, please answer, In the given diagram of triangle ABC, where AB is equal to AC and AD is the median of side BC, when angle B measures 70 degrees, what is the measure of angle BAD? | <answer> 20° </answer> |
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['The diagram consists of two parallel lines, AB and MN. Point C is located on line MN, and point A is connected to points B and C. Line AC intersects line BC at point C.'] then, please answer, In the given diagram, if angle E in triangle ABE measures 25°, and the perpendicular bisector of AE labeled MN intersects BE at point C, and AB is equal to AC, what is the measure of angle BAE? | <answer> 105° </answer> |
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['The diagram consists of a circle labeled as circle O. A line segment AB is tangent to the circle at point D. Point E lies on the extension of line segment AD, and point P lies on the circumference of the circle. Line segment OP intersects line segment AB at point P.'] then, please answer, In the given diagram, point O lies on the side AC of angle BAC, and circle O tangentially touches side AB at point D. The circle also intersects the line segment AO at point E. If point P is located on circle O and angle EPD measures 35.0 degrees, then what is the measure of angle BAC? | <answer> 20° </answer> |
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['The diagram consists of three points, A, B, and C, which form a triangle ABC. Point M is the midpoint of side AB, and point N is the midpoint of side AC. Additionally, there is a line segment MN that connects points M and N.'] then, please answer, Given that angle B measures 20 degrees and angle C measures 25 degrees in the provided figure, if MP and QN bisect AB and AC perpendicularly, what is the measure of angle PAQ? | <answer> 90° </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. Point C lies on line b, and point B lies on line a. There is an angle labeled as angle 1 at point A, which is formed by the intersection of line AC and line a. Angle 2 is also formed by the intersection of line BC and line b.'] then, please answer, In the given illustration, line a is parallel to line b, and in triangle ABC, point C lies on line b. If angle 1 measures 40 degrees and angle 2 measures 20 degrees, what is the degree measure of angle B? | <answer> 60° </answer> |
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["The diagram consists of two squares, ABCD and D'C'EF. Square ABCD is positioned in the top left corner, while square D'C'EF is located below it. The vertices of the squares are labeled as A, B, C, D, E, F, and D'."] then, please answer, In the given rectangular paper ABCD, where AD is parallel to BC and AB is parallel to CD, when the paper is folded along EF, points C and D land in the positions C' and D'. If angle EFB measures 65°, what is the measure of angle AED'? | <answer> 50° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point E is located on line CD such that AE is perpendicular to CD. Point F is the intersection of line AC and line DE.'] then, please answer, In the given diagram, the set square is positioned with its right-angle vertex C coinciding. The intersection of sides AB and CD occurs at point F, and DE is parallel to BC. What is the degree measure of angle AFC? | <answer> 75° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by a transversal line, EF. Point A is connected to points B and C, while point D is connected to points E and F. The angles formed at the intersection points are labeled as angle 1, angle 2, angle 3, and angle 4.'] then, please answer, In the given diagram, if the right angle vertex of the triangle ruler is placed on one side of the straight ruler and angle 1 measures 25 degrees, while angle 2 measures 45 degrees, what is the measure of angle 3? | <answer> 20° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line AC. Point D is located on the extension of line AB. Angle ACD measures 45 degrees, while angle BAC measures 40 degrees.'] then, please answer, As shown in the diagram, line AB is parallel to line CD, and angle A = 40°, angle D = 45°. The degree measure of angle 2 is () | <answer> 85° </answer> |
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['The diagram consists of two intersecting lines, AB and CD, forming an angle of 60 degrees at their intersection point O. Inside the rectangle formed by these lines, there is a smaller triangle labeled as triangle 1. The sides of this triangle are labeled as OA, OB, and OC. Additionally, there is another triangle labeled as triangle 2, which is similar to triangle 1 and shares the same vertex O. Triangle 2 has sides labeled as OD, OE, and OF.'] then, please answer, In the given diagram, a right-angled triangle "board" forms an angle of 60° and has two vertices placed on opposite sides of a rectangle. If angle 1 is 17°, what is the measure of angle 2? | <answer> 13° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is the midpoint of side BC. Point E lies on side AB such that AE is equal to BE. Point F is the foot of the perpendicular from point E to side AC.'] then, please answer, In the given diagram, AF bisects angle BAC and intersects BC at point E. A perpendicular line FD passes through point F and intersects BC at point D. If the measure of angle B is 20 degrees more than angle C, what is the degree measure of angle F? | <answer> 10° </answer> |
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['The diagram consists of a triangle ABC, where points A, B, and C are the vertices of the triangle. Point P is located on the line segment AC.'] then, please answer, In the given triangle ABC, where angle ABC is given as 50 degrees and angle ACB is given as 80 degrees, if the angle bisectors of angle ABC and angle ACB intersect at point P, what is the measure of angle BPC? | <answer> 115° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by a transversal line, EF. Point O is the intersection of lines EF and CD. Angle 1 is formed at point O between lines EF and CD. Angle 2 is also formed at point O between lines EF and CD.'] then, please answer, In the given diagram, position one vertex of a right-angled triangle with a 30° angle on one side of the ruler. If angle 1 measures 43°, what is the measure of angle 2? | <answer> 17° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point D is located on line CD, and point E is located on the extension of line CD beyond point D. Angle 1 is formed by the intersection of line AD and line DE.'] then, please answer, In the given diagram, if angle BAD measures 55 degrees and angle 1 measures 70 degrees, and it is known that angle BAD + angle ADE equals 180 degrees, what is the measure of angle 2? | <answer> 55° </answer> |
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['The diagram consists of two parallel lines, l1 and l2, intersected by line AB at points A and B respectively. Point D is located on line l1, and point C is located on line l2. The angle formed between line AB and line l1 is labeled as angle 1, while the angle formed between line AB and line l2 is labeled as angle 2.'] then, please answer, In the given diagram, it is depicted that line l1 is parallel to line l2, with AB being perpendicular to CD. If angle 1 measures 34°, what is the measure of angle 2? | <answer> 56° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point A is located on line AB, and point D is located on line CD. The angle formed between line AB and the line segment AD is 90 degrees.'] then, please answer, As shown in the figure, ABparallel CD, ADperpendicular AC, angle ACD = 53°. Therefore, the degree of angle BAD is (). | <answer> 37° </answer> |
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['The diagram shows two parallel lines, labeled as line AB and line CD. There are four angles formed by the intersection of these lines: angle 1, angle 2, angle 3, and angle 4. Angle 1 is adjacent to angle 2, and angle 3 is adjacent to angle 4.'] then, please answer, If angle 1 equals angle 3 and angle 2 measures 50 degrees in the given diagram, what is the measure of angle 4? | <answer> 130° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point G lies on line AB, and point E lies on line CD. Line FG intersects line AB at point M and line CD at point N.'] then, please answer, As shown in the diagram, AB is parallel to CD. EF intersects AB at point G. EM bisects angle CEF. Angle FGB is 80°. Therefore, the degree measure of angle GME is (). | <answer> 50° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line BE at point E. Point A is connected to points B and E, while point C is connected to points B and E. Additionally, there is a circle centered at point E that intersects line AB at point D.'] then, please answer, What is the measure of angle ABE in the given diagram where a right triangle with angles of 30 degrees and 45 degrees is placed and DE is parallel to BC? | <answer> 15° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line AE at point E. Point A is connected to points B and C, while point D is connected to points C and E.'] then, please answer, In the given diagram, line AB is parallel to line CD. If angle CAB is bisected by line AE and intersects CD at point E, and angle C measures 100 degrees, what is the measure of angle AED? | <answer> 140° </answer> |
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['The diagram consists of two triangles, ABC and ACD, sharing the common side AC. Triangle ABC is a right triangle with angle BAC being 90 degrees. Point D lies on the extension of line segment BC beyond point C. Angle 1 is formed by lines AD and CD.'] then, please answer, By using the given diagram, how can the degree of angle 1 be calculated if AB is parallel to CD? | <answer> 75° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point D is located on line CD such that angle ADB is a right angle (90 degrees).'] then, please answer, As shown in the figure, line AB is parallel to line CD. Line AD is perpendicular to line BD. The measure of angle ADC is 38 degrees. Therefore, the degree of angle ABD is() | <answer> 52° </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. Point C is located on line b. Point A is connected to points B and C. Angle 1 is formed by the intersection of line AC and line BC. Angle 2 is formed by the intersection of line AB and line AC.'] then, please answer, If line a is parallel to line b and the right angle vertex C of the right triangle ABC lies on line b, and angle 1 measures 54 degrees, what is the degree measure of angle 2? | <answer> 36° </answer> |
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['The diagram consists of two squares, ABCD and EFGH, where points A, B, C, D, E, F, G, and H are the vertices of these squares. The sides of the squares are labeled as AB, BC, CD, DA, EF, FG, GH, and HE.'] then, please answer, If a rectangular strip of paper ABCD is folded along the line AF, and angle ADB measures 32°, with AE being parallel to BD, what is the measure of angle DAF? | <answer> 29° </answer> |
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["The diagram consists of two squares, ABDE and BC'CF, sharing a common side BC. Point E is connected to points A and D, while point F is connected to points B and C'."] then, please answer, When the rectangular paper ABCD is folded so that point D coincides with point B and point C falls on point C', forming the crease EF, and angle ABE measures 30°, what is the degree measure of angle EFC'? | <answer> 120° </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. Inside the diagram, there is an angle labeled as angle 1. Additionally, there is another angle labeled as angle 2.'] then, please answer, In the given diagram, line a and line b are parallel, with the right-angle vertex of triangle board placed on line b. The two perpendicular sides intersect line a. If angle 2 measures 27°, what is the measure of angle 1? | <answer> 63° </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. A transversal line, labeled as line l, intersects both lines a and b at points 1 and 2, respectively.'] then, please answer, As shown in the figure, angle 1 = 110°. To make aparallel b, the size of angle 2 is (?) | <answer> 110° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on the extension of side BC. Point E is the intersection of line AD and line BE. Point F is the midpoint of segment AE. Point G is the midpoint of segment BD. Line EF intersects line GH at point H.'] then, please answer, In the given diagram, if AD is parallel to BC and angle D is equal to angle ABC, point E is located on the side DC. When the line segment AE intersects the extension of BC at point H, and point F is situated on the side AB such that angle FBE is equal to angle FEB, what is the measure of angle BEG if the angle DEH measures 98 degrees? | <answer> 41° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point E is located on line CD, and point F is located on line AB. Line EF intersects line AD at point M.'] then, please answer, If angle BAC is 90 degrees and angle EDF is 90 degrees and DE intersects AC at point M, with angle E measuring 45 degrees and angle C measuring 30 degrees while BC is parallel to EF, what is the measure of angle DMC? | <answer> 105° </answer> |
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['The diagram consists of two parallel lines, l1 and l2, intersected by line MN at points M and N respectively. Point A lies on line l1, while point B lies on line l2. The angles formed between the lines and the transversal MN are labeled as angle 1 and angle 2.'] then, please answer, In the given diagram, if line l1 is parallel to line l2, and angle MAB measures 125 degrees while angle NBA measures 85 degrees, what is the sum of angle 1 and angle 2? | <answer> 30° </answer> |
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['The diagram consists of two parallel lines, labeled as line a and line b. A transversal line, labeled as line c, intersects both lines a and b at points 1 and 2, respectively. The angles formed by the intersection of the transversal with the parallel lines are labeled as angle 1 and angle 2.'] then, please answer, In the diagram, line c intersects lines a and b. If line a is parallel to line b and angle 2 measures 115°, what is the measure of angle 1? | <answer> 65° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point E is located on line AB, and point G is located on line CD. There is an angle labeled as 1 at point E, and another angle labeled as 2 at point G.'] then, please answer, As shown in the figure, AB is parallel to CD, G is a point on line CD, E is a point between line AB and line CD, and F is a point above line AB. Angle F is 40° and angle EGF is 65°. Therefore, the sum of angle 1 and angle 2 is () | <answer> 75° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line OE at point O. Point E lies on the extension of line OA.'] then, please answer, In the provided diagram, if AB is parallel to CD, angle A measures 45 degrees, and angle C is equal to angle E, what is the measure of angle C? | <answer> 22.5° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point M is the midpoint of side AB. Point N is located on side AC such that AN is equal to NC.'] then, please answer, In the given triangle ABC, with angle ABC measuring 50 degrees and angle ACB measuring 100 degrees, a point M moves along ray AB. When a line MN parallel to BC is drawn through point M, and it intersects ray AC at point N, the line BN is connected. If there are two congruent angles in triangle BMN, what is the degree measure that angle MNB cannot be? | <answer> 30° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line AE at point A. Point G lies on the extension of line AE beyond point E.'] then, please answer, In the given diagram, if line AB is parallel to line CD and line AG bisects angle BAE, and angle CEF measures 62 degrees, what is the degree measure of angle FAG? | <answer> 149° </answer> |
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['The diagram consists of four straight lines labeled as l1, l2, l3, and l4. These lines intersect at various points, forming angles.'] then, please answer, In the given diagram, lines l1, l2, and l3 intersect at a single point, and line l4 is parallel to line l1. If the measure of angle 1 is 120° and the measure of angle 2 is 80°, what is the degree measure of angle 3? | <answer> 40° </answer> |
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['The diagram consists of two triangles, ABC and PBC, sharing the common side BC. Point A is connected to points B and C, while point P is connected to points B and C as well. The line segment AP intersects the line segment BD at point D.'] then, please answer, In the given figure, the angle bisectors of angle ABD and angle ACD meet at point P. If angle A measures 48 degrees and angle D measures 10 degrees, what is the measure of angle P? | <answer> 19° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point E is located on line CD, and point A is connected to points D and E.'] then, please answer, In the given diagram, if BC is parallel to DE and angle 1 measures 110°, while angle AED measures 80°, what is the measure of angle A? | <answer> 30° </answer> |
Subsets and Splits