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['The diagram consists of two lines, AB and CD, intersecting at point O. Angle 1 is formed between line OA and the intersection point O. Angle 2 is formed between line OB and the intersection point O.'] then, please answer, In the given diagram, if angle 1 has a measure of 35.0 degrees, what is the measure of angle 2? | <answer> 145° </answer> |
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['The diagram consists of a right triangle ABC, where angle C is a right angle. Point D lies on the line segment BC and is not at point B or C. Point E lies on the line segment AD. The diagram also includes lines DE and AE.'] then, please answer, In the given diagram, consider right triangle ABC where angle C equals 90 degrees. The perpendicular bisector of side AB, labeled as DE, intersects BC at point D and intersects AB at point E. If AD divides angle CAB into two angles and the ratio of angle CAD to angle BAD is 0.4, what is the measure of angle ADC? | <answer> 75° </answer> |
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['The diagram consists of two parallel lines, l1 and l2, intersecting line BC at points A and B respectively. Point C is located on the extension of line BC.'] then, please answer, As shown in the figure, line l1 is parallel to line l2, and triangle ABC is an equilateral triangle. If angle 1 = 40°, then the size of angle 2 is () | <answer> 80° </answer> |
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['The diagram consists of two triangles, ABC and BDC, sharing the common side BC. Point D lies on the line segment AB.'] then, please answer, In the given triangle ABC, if line BD is perpendicular to AC and also bisects it, and angle A measures 20 degrees, what is the measure of angle CBD? | <answer> 70° </answer> |
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['The diagram consists of two parallel lines, AB and CD. Point A is connected to points M and N on line AB. Point P is the intersection of line AP and line CD. Point Q is the intersection of line AQ and line BC.'] then, please answer, In the given diagram, if angle B measures 20° and angle C measures 30°, and MP and QN bisect AB and AC perpendicularly, what is the measure of angle PAQ? | <answer> 80° </answer> |
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['The diagram consists of two lines, AB and CD, intersecting at point C. Point D lies on line AB.'] then, please answer, What is the measure of angle ADC in right triangle ABC if angle ACB is 90 degrees, angle A is 52 degrees, and a circle with point B as the center and BC as the radius intersects AB at point D? | <answer> 109° </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. Line DE is parallel to side AC and intersects side AB at point E. Point F is the intersection of line EF and side AC.'] then, please answer, What is the degree measure of angle CFA in triangle ABC, where AB is equal to AC, angle BAC measures 100°, AD is the median of side BC, CE bisects angle BCA, and intersects AB at point E, and AD intersects CE at point F? | <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 BC.'] then, please answer, In the given illustration, triangle ABC is depicted with BA being equal to BC. The line segment DE serves as the perpendicular bisector of side AB, intersecting BC and AB at points D and E, respectively. If AD functions as the angle bisector of angle BAC, what is the degree measure of angle B? | <answer> 36° </answer> |
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['The diagram shows a right triangle ABC with vertices A, B, and C. Point D is located on the hypotenuse AB such that CD is perpendicular to AB. The length of side AC is 3 units, and the length of side BC is 4 units.'] then, please answer, What is the measure of angle A in right triangle ABC, where angle ACB is 90 degrees, and an arc is drawn with point B as the center and BC as the radius, intersecting AB at point D, and angle ACD measures 20 degrees? | <answer> 50° </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 such that AD is perpendicular to BC.'] then, please answer, In the given triangle ABC, where AB is equal to AC, and AD is the median of side BC, with angle B measuring 25 degrees, what is the measure of angle BAD? | <answer> 65° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there are three points labeled as A, B, and C. Point D is located on the extension line of segment BC.'] then, please answer, In the provided figure, the quadrilateral ABCD is inscribed in circle O. If one of its exterior angles, DCE, measures 62.0, what is the measure of angle BOD? | <answer> 124° </answer> |
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['The diagram consists of a triangle OBC, where angle BOC is 45 degrees and angle AOB is 30 degrees. Point D lies on the extension of line segment OB, and point E lies on the extension of line segment OC.'] then, please answer, If a student utilizes a set square with acute angles measuring 30 degrees and 45 degrees and aligns the right-angled vertices, and angle DEB is 60 degrees, what is the measure of angle AOC? | <answer> 45° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line OE at points O and E. Point A is connected to point B, while point C is connected to point D. Additionally, there is a line segment OC connecting points O and C.'] then, please answer, In the given figure, point O is the intersection of AE and CD, with AB being parallel to CD. If OC is equal to OE and angle A measures 50 degrees, what is the measure of angle C? | <answer> 25° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point O is located inside the triangle. Additionally, there is a line segment OD that passes through point D on side AB and intersects side AC at point E.'] then, please answer, In the given diagram, triangle ABC is equilateral with BO as the median line, and BA extended to point D such that AD is equal to AO. What is the degree measure of angle DOB? | <answer> 120° </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 CD, while angle 2 is formed between line AC and line AB.'] then, please answer, If AB is parallel to CD and AC equals BC, and angle 1 measures 70 degrees in the given diagram, what is the degree measure of angle 2? | <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. Additionally, there is a line segment DE that passes through point D and intersects the side AB at point E.'] then, please answer, In the given diagram, point D lies on AC, while point E lies on AB. It is also given that AB is equal to AC, and BC is equal to BD, and AD is equal to DE, which also equals BE. What is the measure of angle A? | <answer> 45 </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. Point F is the intersection of line segments DE and BC.'] then, please answer, What is the sum of angle A, angle B, angle C, angle D, angle E, and angle F in the given equation? | <answer> 360° </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 AB at point E and line CD at point F.'] then, please answer, In the given diagram, triangle ABC is depicted with angle ACB measuring 120 degrees. If square ACDE and regular pentagon BCFGH are constructed with sides AC and BC, what is the measure of angle DCF? | <answer> 42° </answer> |
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['The diagram shows a right triangle with one angle measuring 30 degrees and the other two angles measuring 60 degrees. The hypotenuse of the triangle is labeled as AB, and the legs are labeled as AC and BC. The angle opposite to side AC is labeled as angle 1.'] then, please answer, When Xiaoming was folding a rectangular piece of paper into a regular pentagon, what is the measure of angle 1 in the figure? | <answer> 72° </answer> |
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['The diagram consists of two parallel lines, AB and MN, intersected by line l at points D and E. Point F lies on the extension of line CD. Line EF intersects line l at point G.'] then, please answer, As shown in the diagram, the sides CD and FG of the regular pentagon ABCDE and the regular hexagon EFGHMN are on the line l. The pentagon is on the left side of the hexagon, and both polygons are on the same side of the line l. Therefore, the size of angle DEF is (). | <answer> 48° </answer> |
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['The diagram shows a circle labeled as circle O. On the circumference of the circle, there are three points labeled A, B, and C. The line segment AB is a diameter of the circle. The line segment AC intersects the circle at point C and extends to intersect the circle again at point B.'] then, please answer, Given that points A, B, and C lie on circle O and angle AOB measures 80.0 degrees, what is the measure of angle ACB? | <answer> 40° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral. Point E is located on side AB, and point F is located on side CD. Additionally, there is a line segment EF that connects points E and F.'] then, please answer, If quadrilateral ABCD is depicted in the figure, with AD equal to BC and point P being the midpoint of diagonal BD while E and F are the midpoints of AB and CD respectively, what is the measure of angle PEF if angle EPF is 130 degrees? | <answer> 25° </answer> |
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['The diagram consists of two parallel lines, l1 and l2. Point A is located on line l1, while point B is located on line l2. Point C is the intersection of lines AB and CD. Point D is also located on line l2. Line CD intersects line l1 at point E.'] then, please answer, As shown in the figure, pentagon ABCDE is a regular pentagon. If l1parallel l2, the value of angle 1 - angle 2 is () | <answer> 72° </answer> |
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['The diagram consists of a quadrilateral ABCD. Point E is located on the line segment BC, and point D is connected to points A and C.'] then, please answer, In the given parallelogram ABCD, where angle B measures 60 degrees, the angle bisector of angle BAD intersects BC at point E. If the measure of angle AED is 80 degrees, what is the degree measure of angle EAC? | <answer> 20° </answer> |
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['The diagram consists of a triangle ABC with vertices A, B, and C. Point D is located on side AB, and point E is located on side AC. Line DE is parallel to side BC.'] then, please answer, If points D and E are the midpoints of the sides AB and AC of triangle ABC and connected, and angle B measures 50 degrees while angle A measures 60 degrees, what is the degree measure of angle AED? | <answer> 70° </answer> |
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['The diagram consists of a parallelogram ABCD. Point A is connected to points B and D, while point C is connected to points B and D. Additionally, there is a line segment AC connecting points A and C.'] then, please answer, As shown in the figure, in ABCD, angle ADC = 135° and angle CAD = 23°, then angle CAB is equal to (). | <answer> 22° </answer> |
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['The diagram consists of a parallelogram ABCD. Point E is located on the line segment AD, and there is a right angle at point E.'] then, please answer, In the given diagram, quadrilateral ABCD is depicted with AE perpendicular to CD. If angle B measures 70 degrees, what is the degree measure of angle DAE? | <answer> 20° </answer> |
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['The diagram consists of a quadrilateral ABCD. Points A, B, C, and D are the vertices of the quadrilateral.'] then, please answer, In the given diagram depicting quadrilateral ABCD, if angle ABC measures 125 degrees and angle CAD measures 21 degrees, what is the measure of angle CAB? | <answer> 34° </answer> |
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['The diagram consists of a quadrilateral ABCD. Point E is located on the line segment AB, and point D is located on the line segment BC.'] then, please answer, What is the measure of angle E in triangle BCDE if angle A in triangle ABC measures 40 degrees and AB is equal to AC? | <answer> 70° </answer> |
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['The diagram consists of a parallelogram ABCD. Point A is located at the bottom left corner, point B is at the bottom right corner, point C is at the top right corner, and point D is at the top left corner.'] then, please answer, If angle A measures 60 degrees in parallelogram ABCD, what is the degree measure of angle C? | <answer> 60° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line EF at points E and D. Point A is connected to point B, while point C is connected to point F.'] then, please answer, In the given diagram, if in triangle ABC, point D is the midpoint of AC and point E is the midpoint of AB, and point F lies on the extension of BC, and if angle A measures 35° and angle AED measures 30°, then what is the degree measure of angle ACF? | <answer> 65° </answer> |
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['The diagram consists of a parallelogram ABCD. Point E is located on the line segment AB, dividing it into two equal parts.'] then, please answer, In the given diagram of quadrilateral ABCD, the angle bisector BE intersects DC at point E. If angle A measures 60°, what is the measure of angle DEB? | <answer> 120° </answer> |
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['The diagram consists of a parallelogram ABCD. Point E is located on the line segment AD, and point F is located on the line segment BC. The line segments DE and EF are perpendicular to each other.'] then, please answer, As shown in the figure, in ABCD, BD = BC, AE is perpendicular to BD, and the foot is E. If angle C = 55°, then the degree of angle EAB is (). | <answer> 35° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral. The sides AB, BC, CD, and DA form the four edges of the quadrilateral.'] then, please answer, What is the measurement of angle B in parallelogram ABCD if the sum of angles A and C is 130 degrees, as depicted in the diagram? | <answer> 115° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral.'] then, please answer, If angle B in the parallelogram ABCD is 70 degrees, what is the measure of angle D? | <answer> 70° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral. The sides AB and CD are parallel to each other, while the sides AD and BC are also parallel to each other.'] then, please answer, In the given diagram, if the sum of angles A and C in parallelogram ABCD equals 160°, what is the measure of angle B? | <answer> 100° </answer> |
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['The diagram shows a quadrilateral ABCD, where points A, B, C, and D represent the vertices of the shape. The sides AB, BC, CD, and DA connect these vertices in sequence.'] then, please answer, In the given parallelogram ABCD, if the sum of angle B and angle D measures 100°, what is the measure of angle A? | <answer> 130° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D represent the vertices of the quadrilateral. The sides AB, BC, CD, and DA connect these vertices in sequence.'] then, please answer, In the given figure, if in quadrilateral ABCD, angle B added to angle D equals 140 degrees, what is the measure of angle C? | <answer> 110° </answer> |
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['The diagram consists of a parallelogram ABCD. Point E is located on the line segment AD, and point F is located on the line segment BC. The lines AE and BF intersect at point G.'] then, please answer, As shown in the diagram, in the parallelogram ABCD, angle DBC = 25°, angle BAD = 115°, then angle BDC = (). | <answer> 40° </answer> |
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['The diagram shows two parallel lines, line 1 and line 2, intersected by a transversal line. There are four angles formed at the intersection: 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 the sum of angle 2, angle 3, and angle 4 is 320.0 degrees as indicated in the figure, what is the measure of angle 1? | <answer> 40度 </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral.'] then, please answer, In the given parallelogram ABCD, if angle A measures 150 degrees, what is the degree measure of angle C? | <answer> 150° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral.'] then, please answer, In the given diagram illustrating quadrilateral ABCD, if the sum of angle B and angle D is 200 degrees, what is the measure of angle A? | <answer> 80° </answer> |
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['The diagram consists of a parallelogram ABCD. Point E is located on the line segment AD, and point F is located on the line segment BC. The lines DE and EF intersect at point E.'] then, please answer, In the given diagram of quadrilateral ABCD, where AB equals BD and point E lies on BD with CE measuring the same as CB, if angle ADB is 65 degrees, what would be the measure of angle DCE? | <answer> 15° </answer> |
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['The diagram consists of a parallelogram ABCD. Point M is located on the extended line of side AB, and point D is connected to point M.'] then, please answer, In the given diagram, for the quadrilateral ABCD, a point M is positioned on the extension of side AB. If angle D measures 120 degrees, what is the measure of angle CBM? | <answer> 60° </answer> |
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['The diagram consists of a parallelogram ABCD. Points A, B, C, and D represent the vertices of the parallelogram.'] then, please answer, In the given figure, if the sum of angles A and C in quadrilateral ABCD is 110 degrees, what is the measure of angle B? | <answer> 125° </answer> |
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['The diagram consists of a parallelogram ABCD. Point E is located on the extension of side DC.'] then, please answer, What is the measure of angle B in quadrilateral ABCD if point E lies on the extension of side DC, AE equals DE, and angle E measures 46 degrees? | <answer> 67° </answer> |
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['The diagram shows a quadrilateral ABCD, where points A, B, C, and D are the vertices of the shape. The sides AB and CD are parallel to each other, as well as the sides AD and BC. This indicates that the quadrilateral is a parallelogram.'] then, please answer, In the given figure for quadrilateral ABCD, if angle A measures twice the size of angle B, what is the measure of angle D? | <answer> 60° </answer> |
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['The diagram consists of a parallelogram ABCD. Points A, B, C, and D represent the vertices of the parallelogram.'] then, please answer, What is the measure of angle D in parallelogram ABCD if the sum of angle A and angle C is 120 degrees, as depicted in the diagram? | <answer> 120° </answer> |
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['The diagram consists of a parallelogram ABCD. Point C is connected to points A and B, while point D is connected to points B and C. Point E lies on the extension of line segment BC. The angle formed by lines AC and CE is labeled as angle 1.'] then, please answer, If one side of quadrilateral ABCD, BC, is extended to point E and angle A measures 110° in the given diagram, what is the measure of angle 1? | <answer> 70° </answer> |
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['The diagram consists of two triangles, OAB and OCD, sharing the common side OC. Point D lies on the line segment AB.'] then, please answer, If angle AOC is measured at 130.0 degrees in the figure depicting a set of triangular plates placed on a desktop (with the right-angle vertices coinciding), what is the measure of angle BOD? | <answer> 50° </answer> |
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['The diagram consists of a parallelogram ABCD. Point E is located on the line segment BC, dividing it into two equal parts.'] then, please answer, In the parallelogram ABCD, point E lies on side BC, and the line segment AE is drawn. If AE bisects angle BAD and angle D measures 58 degrees, what is the measure of angle AEC? | <answer> 119° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral. Point E is located on the line segment AB.'] then, please answer, In the given diagram of triangle ABC where AB is equal to AC, point D lies on side AC. By constructing quadrilateral BCDE with CB and CD as sides, if angle A measures 40°, what is the degree measure of angle E? | <answer> 70° </answer> |
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['The diagram consists of a parallelogram ABCD. Point C is connected to points A and B, while point D is connected to points B and C. Point E lies on the extension of line segment BC. The angle formed by lines AC and CE is labeled as angle 1.'] then, please answer, As shown in the diagram, extend one side of ABCD, BC, to point E. If angle 1 = 80°, then angle A is equal to () | <answer> 100° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral. Point E is located on side AB, and point F is located on side CD. Additionally, there is a line segment EF that intersects side AD at point H.'] then, please answer, In the given diagram, ABCD forms a parallelogram. At point E, DE is perpendicular to BC, and at point F, BF is perpendicular to CD. If DE and BF intersect at point H, and angle A measures 60°, then what is the measure of angle EHF? | <answer> 120° </answer> |
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['The diagram consists of a quadrilateral ABCD, where points A, B, C, and D are the vertices of the quadrilateral. Point E is located on the extension of side BC.'] then, please answer, In the given diagram, the quadrilateral ABCD is depicted. If the measure of angle A is 100 degrees and BC is extended to point E, what is the measure of angle DCE? | <answer> 80° </answer> |
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['The diagram consists of two triangles, ABC and DEF, sharing the side BC. Point D is located on line segment AB, and point E is located on line segment BC. Point F is located on line segment AC.'] then, please answer, If triangle ABC has angle B measuring 70 degrees and angle C measuring 50 degrees, and points D, E, and F are the midpoints of sides AB, BC, and CA respectively, what is the measure of angle DEF? | <answer> 60° </answer> |
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['The diagram shows a quadrilateral ABCD, where points A, B, C, and D are the vertices of the shape. The sides AB and CD are parallel to each other, as well as the sides AD and BC. This indicates that the quadrilateral is a parallelogram.'] then, please answer, As shown in the figure, in ABCD, angle A+angle C=140°, then the measure of angle B 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 side AB of the triangle. Point E is the midpoint of the line segment CD.'] then, please answer, In the provided figure, the perpendicular bisector of BC intersects AB and BC at point D and E, respectively. It also connects CD. If AC measures the same as DC and angle B is 25.0 degrees, what is the degree measure of angle ACD? | <answer> 80° </answer> |
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['The diagram consists of two parallel lines, AB and CD, intersected by line AC. Point B is located on line AB, and point C is located on line CD. Angle 1 is formed at the intersection of lines AB and AC, while angle 2 is formed at the intersection of lines CD and AC. The measure of angle A is given as 30 degrees.'] then, please answer, In the given triangle ABC, if angle A measures 30 degrees, what is the sum of angle 1 and angle 2? | <answer> 210° </answer> |
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['The diagram shows a triangle with two circles inscribed within it. The first circle is located at the top of the triangle, while the second circle is located at the bottom. Both circles are tangent to the sides of the triangle and to each other.'] then, please answer, What is the measure of angle α when a set of protractors are stacked together as shown in the diagram? | <answer> 75° </answer> |
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['The diagram consists of two triangles, ABC and DEF, sharing a common side DE. Point D lies on the line segment AB, and point F lies on the line segment BC. The diagram also includes points A, B, C, D, E, and F.'] then, please answer, As shown in the figure, if angle A = 20°, angle B = 45°, angle C = 35°, then angle DFE is equal to (). | <answer> 100° </answer> |
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['The diagram consists of two triangles, ΔADE and ΔABC. Triangle ΔADE is positioned inside triangle ΔABC. Point D lies on the line segment AC, and point E lies on the line segment AB. The vertices of triangle ΔADE are labeled as A, D, and E, while the vertices of triangle ΔABC are labeled as A, B, and C.'] then, please answer, In the given diagram, if triangle ABC is folded along DE and point A ends up outside quadrilateral BCDE, with angle 1 measuring 70° and angle 2 measuring 152°, what is the measure of angle A? | <answer> 42° </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, In the given diagram, BD is the angle bisector of triangle ABC. If angle DBA is 30 degrees and angle ADB is 80 degrees, what is the measure of angle C? | <answer> 50° </answer> |
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['The diagram shows a triangle ABC with vertices A, B, and C. Point D is the midpoint of side AB, and point E is the midpoint of side AC. Point F is the midpoint of side BC. The line segments AD, BE, and CF intersect at point O.'] then, please answer, What is the sum of the measures of angles A, B, C, D, E, and F in the given diagram? | <answer> 360° </answer> |
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['The diagram consists of two intersecting circles, circle A and circle B. Circle A is tangent to both the x-axis and the y-axis at points A and C respectively. Circle B is also tangent to both the x-axis and the y-axis at points B and D respectively. The line segment AB intersects the line segment CD at point P.'] then, please answer, BP is the bisector of angle ABC, CP is the bisector of the adjacent supplementary angle of angle ACB. angle ABP = 20°, angle ACP = 50°, then angle P = ( ). | <answer> 30° </answer> |
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["I'm sorry, but as an AI language model, I don't have access to any specific image or diagram that you may be referring to. Could you please provide me with more information about the diagram so that I can assist you better?"] then, please answer, What is the measure of angle 2 if a triangle ruler with a 30.0 angle is placed on the ruler and angle 1 measures 25.0 degrees in the given figure? | <answer> 35° </answer> |
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['The diagram shows a quadrilateral ABCD, where points A and B are connected by line segment AB. Point D is located on the extension of line segment AB beyond point B.'] then, please answer, What method can be used to determine the measurement of angle C in triangle ABC before any damage occurs? | <answer> 65° </answer> |
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['The diagram consists of two triangles, ABC and DEF, sharing a common side BC. Point D is located on the extension of line segment AB, and point E is located on the extension of line segment AC.'] then, please answer, As shown in the diagram, given angle A = 60°, the sum of the degrees of angle D + angle E + angle F + angle G is () | <answer> 240° </answer> |
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['The diagram consists of a pentagon labeled ABCDE, where vertices A, B, C, D, and E are connected in sequence. Point P is located outside the pentagon. Additionally, there is a line segment FG that intersects the sides AB and CD at points G and F respectively.'] then, please answer, In the given heptagon ABCDEFG, the lines EF and BA are extended to intersect at point P. If the total of the exterior angles of angles ABC, BCD, CDE, and DEF is 230°, what is the measurement of angle P? | <answer> 50° </answer> |
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['The diagram consists of two triangles, ΔABC and ΔADE, sharing the common side AD. Point D lies on the line segment BC, and point E lies on the line segment AC. The diagram also includes points A, B, C, D, and E.'] then, please answer, In the provided diagram, if angle A measures 70°, angle B measures 40°, and angle C measures 30°, what is the total measure of angles D and E? | <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 extension of line segment BC.'] then, please answer, In the given diagram, points B, C, and D are aligned in a straight line. If angle B measures 56° and angle ACD measures 120°, what is the measure of angle A? | <answer> 64° </answer> |
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['The diagram shows a triangle ABC with vertices A, B, and C. Point O is the circumcenter of the triangle, which is the point where the perpendicular bisectors of the sides of the triangle intersect.'] then, please answer, Triangle ABC's interior angle bisectors OB and OC intersect at point O. If angle A = 110°, then angle BOC = () | <answer> 145° </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 AB beyond point B. There is an angle labeled as alpha, which is formed between line segment AD and line segment AC. Additionally, there is a circle inscribed within triangle ABC.'] then, please answer, What is the measure of angle α in the triangle board puzzle activity stacked by Xiaoming according to the given diagram? | <answer> 105° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there is a point labeled as A. A line segment AB is drawn from point A to point B on the circumference. Another line segment AC is drawn from point A to a point C on the circumference. Point O is located at the center of the circle.'] then, please answer, In the given diagram, circle O has chord AB and tangent AC with point A as the tangent point. Additionally, line BC passes through the center of the circle. If angle B measures 25.0, what is the measure of angle C? | <answer> 40° </answer> |
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['The diagram shows a right triangle ABC, where angle B is a right angle. The vertices A, B, and C are connected by straight lines. The lengths of the sides AB and BC are equal to 3 units each. The length of side AC is 5 units.'] then, please answer, In the provided grid diagram, the vertices of triangle ABC are situated on the grid points, and the side length of each small square is 1. What is the measure of angle ABC? | <answer> 135° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there are four points labeled A, B, C, and D in a clockwise direction. The line segment AB is a diameter of the circle. Point E lies on the line segment AB, and point O is the center of the circle.'] then, please answer, In the given diagram, if BD is the diameter of circle O, and BD is perpendicular to AC at point E, with angle AOC measuring 100 degrees, what is the measure of angle OCD? | <answer> 25° </answer> |
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['The diagram shows a circle labeled as circle O. Inside the circle, there is a triangle ABC. Point A is connected to points B and C, forming the sides of the triangle. The center of the circle is marked as point O.'] then, please answer, If BC is the diameter of circle O and angle AOC measures 58 degrees, what is the measure of angle A? | <answer> 29° </answer> |
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["I'm sorry, but I cannot see any diagram attached to your question. Could you please provide me with the diagram so that I can assist you better?"] then, please answer, As shown in the figure, triangle ABC is circumscribed to circle O and angle A is 40°. Therefore, the degree of angle BCO is () | <answer> 50° </answer> |
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['The diagram shows a circle labeled as circle O. Inside the circle, there is a triangle labeled as triangle ABC. Point A is connected to points B and C by line segments AB and AC respectively. The center of the circle is marked as point O.'] then, please answer, In the given diagram, if angle C in circle O measures 20 degrees and angle B is 35 degrees, what is the measure of angle A? | <answer> 15° </answer> |
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['The diagram consists of a circle denoted as circle O. On the circumference of this circle, there are four points labeled A, B, C, and D in a clockwise direction. Additionally, there is another point E on the extended line of AB.'] then, please answer, In the given diagram, if AB is the diameter of circle O and points C, D, and E are located on circle O, with AD equal to CD and angle E measuring 70°, what is the measure of angle ABC? | <answer> 40° </answer> |
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['The diagram consists of a circle denoted as circle O. On the circumference of the circle, there is a point labeled A. From point A, two line segments are drawn to points B and C on the circumference. Additionally, there is a line segment connecting points O and A.'] then, please answer, In the given diagram, if triangle ABC is inscribed in circle O and the measure of angle ABO is 40 degrees, what is the measure of angle ACB? | <answer> 50° </answer> |
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['The diagram shows a circle labeled as circle O. On the circumference of the circle, there are four points labeled A, B, C, and D in clockwise order. Point E is located outside the circle on the extension of line segment BC.'] then, please answer, If quadrilateral ABCD is circumscribed around circle O and one of its exterior angles, angle DCE, measures 115°, then what is the measure of the other exterior angle, angle DAF? | <answer> 65° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there is a point named A. From point A, two tangents are drawn to the circle, intersecting at point P. Point C lies on the line segment AB. Additionally, there is a line segment OC that connects points O and C.'] then, please answer, In the given diagram, all the points A, B, C, D, and P are located on the circle O. The line OC is perpendicular to AB. When angle ADC measures 15° (where 0° < α < 90°), what is the measure of angle APB? | <answer> 150° </answer> |
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['The diagram consists of a cone labeled as ABC, where point A is the apex of the cone and points B and C lie on the base circle. The base circle has a center at point O.'] then, please answer, What is the lateral area of the conical funnel made by Xiao Ming in the comprehensive practical activity class if the bottom radius is 6.0 and the height is 8.0? | <answer> 60πcm </answer> |
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["I'm sorry, but I cannot provide 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, In the given diagram, AB is the diameter of circle O, and points C and D lie on circle O. If angle D measures 120°, what is the measure of angle CAB? | <answer> 30° </answer> |
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['The diagram consists of a circle denoted as circle O. On the circumference of this circle, there are four points labeled A, B, C, and D. Point E is located outside the circle on the extension of line segment AB.'] then, please answer, If CD is the diameter of circle O and chord DE is parallel to radius OA, while arc CE measures 92 degrees, what is the measure of angle C? | <answer> 23° </answer> |
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['The diagram shows a circle labeled as circle O. On the circumference of the circle, there is a point labeled as A. From point A, two lines are drawn to intersect the circle at points B and C. The line segment AB intersects the line segment AC at point A. Additionally, there is a line segment AO that connects point A to the center of the circle, labeled as point O.'] then, please answer, If point A, B, and C are on circle O and angle B measures 32 degrees, what is the measure of angle OAC? | <answer> 58° </answer> |
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['The diagram consists of a circle denoted as circle O. On the circumference of this circle, there are three points labeled A, B, and C.'] then, please answer, In the provided diagram, points A, B, and C lie on the circle O in the given order. If the difference between angle B and angle A is 40 degrees, what is the measure of angle AOB? | <answer> 80° </answer> |
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['The diagram consists of a circle labeled as circle O. Inside the circle, there is a quadrilateral labeled ABCD. The vertices A, B, C, and D are connected by straight lines to form the quadrilateral.'] then, please answer, Given the figure with points A, B, C, D, and E all lying on circle O, and AC equal to AE, if angle B measures 128 degrees, what is the degree measure of angle D? | <answer> 104° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there is a point labeled as A. From point A, two lines are drawn to intersect the circle at points B and C.'] then, please answer, As shown in the diagram, point A, B, and C are three points on circle O. If angle AOB = 66°, then the degree of angle C is () | <answer> 33° </answer> |
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['The diagram consists of a circle denoted as circle O. On the circumference of this circle, there are four points labeled A, B, C, and D.'] then, please answer, In the given diagram, if quadrilateral ABCD is inscribed in circle O and angle BCD measures 140°, what is the degree measure of angle BOD? | <answer> 80° </answer> |
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['The diagram shows a circle labeled as circle O. On the circumference of the circle, there is a point labeled as A. Another point on the circumference is labeled as B. The line segment AB is a chord of the circle.'] then, please answer, Given that points A, B, and C all lie on circle O, and angle BOC measures 100 degrees, what is the measure of angle BAC? | <answer> 50° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there are three points labeled as A, B, and C. Additionally, there is another point labeled as D on the circumference of the circle.'] then, please answer, As shown in the figure, AB is the diameter of circle O. C and D are two points on circle O. Connect AC, CD, and AD. If angle ADC = 75°, then the degree of angle BAC is (). | <answer> 15° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there is a point named A. From point A, two lines are drawn to intersect the circle at points B and C. Additionally, there is another line segment connecting points D and B.'] then, please answer, In the given diagram, circle O has line AB as its diameter. Point D lies on circle O, and OD and BD are connected. A tangent is drawn to circle O passing through point D, and it intersects the extension of line BA at point C. If angle C measures 40°, what is the measure of angle B? | <answer> 25° </answer> |
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['The diagram consists of two concentric circles. The larger circle is centered at point O, and the smaller circle is also centered at point O but has a smaller radius than the larger circle. The line segment AB represents the chord of the larger circle that is tangent to the smaller circle at point C.'] then, please answer, ? | <answer> 100π平方米 </answer> |
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['The diagram consists of a circle denoted as circle O. On the circumference of this circle, there are three points labeled A, B, and C. Point D is located on the extension of line segment AB beyond point A.'] then, please answer, As shown in the figure, quadrilateral ABCD is inscribed in circle O, with DA=DC. If angle CBE=45°, then the measure of angle DAC is () | <answer> 67.5° </answer> |
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['The diagram shows a circle labeled as circle O. On the circumference of the circle, there are three points labeled as A, B, and C. Point O is the center of the circle.'] then, please answer, What is the measure of angle AOB if angle ACB measures 36 degrees and points A, B, and C are all located on circle O? | <answer> 72° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there is a point named A. From point A, two lines are drawn: one line intersects the circle at points B and D, while the other line intersects the circle at points C and E. The line segment AB is perpendicular to the line segment CD.'] then, please answer, If in the given figure, circle O is the circumcircle of triangle ABC, and angle A measures 62°, and E is the midpoint of BC, what is the degree measure of angle D where OE, extended, intersects circle O at point D, and BD is then connected? | <answer> 59° </answer> |
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['The diagram shows a circle labeled as circle O. Inside the circle, there is a triangle labeled ABC. Point A is located on the circumference of the circle, and points B and C are also on the circumference. The center of the circle is marked as point O.'] then, please answer, In the given diagram of circle O, if the length of AB is equal to the length of AC and angle B measures 70 degrees, what is the measure of angle A? | <answer> 40° </answer> |
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['The diagram consists of a circle labeled as circle O. On the circumference of the circle, there are three points labeled A, B, and C. Point D is located on the extended line of segment AB.'] then, please answer, The degree of angle ADE is (). | <answer> 100° </answer> |
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