hiyouga/geometry3k · Datasets at Hugging Face

images images listlengths 1 1	problem stringlengths 13 234	answer stringlengths 1 34
	<image>Find $x$ in the figure.	90
	<image>A square with side length of $9$ inches is inscribed in $\odot J$. Find the exact circumference of $\odot J$.	9 \sqrt 2 \pi
	<image>Find $x$.	3
	<image>If QRST is a parallelogram, find $x$	5.4
	<image>For trapezoid QRST, M and P are midpoints of the legs. If TS = 2x, PM = 20, and QR = 6x, find x.	5
	<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.	80
	<image>Find x.	14
	<image>Find $m \widehat {PO}$.	112
	<image>Find the perimeter of the triangle. Round to the nearest tenth if necessary.	36
	<image>Find $m\angle D$	117
	<image>Points $P$, $Q$, and $R$ are the midpoints of $\overline{J K}$, $\overline{K L}$, and $\overline{J L}$, respectively. Find $x$ .	5.5
	<image>Find $h$ in each triangle.	\frac { 15 \sqrt 2 } { 2 }
	<image>Find $XY$.	7
	<image>Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.	4.1
	<image>Find the scale factor from $W$ to $W'$.	0.75
	<image>Find $U B$ if $\triangle R S T \sim \triangle U V W, \overline{T A}$ and $\overline{WB}$ are medians, $T A=8$, $R A=3, W B=3 x-6,$ and $U B=x+2$	36
	<image>$UJ=9, VJ=3$, and $ZT=18$. Find $JT$.	6
	<image>If $MNPQ \sim XYZW,$ find the perimeter of $XYZW$.	17
	<image>Find the area of the figure.	64
	<image>Find x	5 \sqrt { 2 }
	<image>Find $m \angle 5$.	85
	<image>Quadrilateral $WXZY$ is a rhombus. If $m \angle XZY=56$, find $m \angle YWZ$.	28
	<image>Find the area of the figure in feet. Round to the nearest tenth, if necessary.	14.4
	<image>Find $x$.	21
	<image>In $\odot P, P D=10, P Q=10,$ and $Q E=20$, find PE	10 \sqrt { 5 }
	<image>If $WXYZ$ is a kite, find $ZY$.	8 \sqrt { 10 }
	<image>Find the area of the regular polygon. Round to the nearest tenth.	15.6
	<image>If $m \angle AFB = 8x - 6$ and $m \angle BFC = 14x + 8$, find the value of $x$ so that $\angle AFC$ is a right angle.	4
	<image>Find $x$.	170
	<image>Find $x$.	11.2
	<image>Find the area of the figure. Round to the nearest hundredth, if necessary.	4
	<image>Find the area of the figure. Round to the nearest tenth if necessary.	50
	<image>Find x	24
	<image>Find x.	\frac { 13 \sqrt { 2 } } { 2 }
	<image>Find the measure of $\angle 1$.	56
	<image>Find $y$.	3
	<image>Use parallelogram ABCD to find $m\angle BCD$	52
	<image>In $\odot A, m \angle E A D=42$. Find $m \widehat{C D}$	138
	<image>For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.	\frac { \sqrt { 3 } } { 2 }
	<image>Find x.	4 \sqrt { 13 }
	<image>Find $x$. (Hint: Draw an auxiliary line.)	130
	<image>Find z	2 \sqrt { 6 }
	<image>In $\odot F$, find $m \widehat {AED}$.	153
	<image>Find $y$ in the figure.	26.3
	<image>For trapezoid $ABCD$, $S$ and $T$ are midpoints of the legs. If $AB=3x$, $ST=15$, and $CD=9x$, find $x$.	2.5
	<image>If $BT = 5$ and $TC = 8$, find $CD$.	\sqrt { 89 }
	<image>If $QR=2$, $XW=12$, $QW=15$, and $ST=5$, find $RS$.	8
	<image>In $\odot W$, $\widehat {RS} \cong \widehat {TV}$. Find $RS$.	11
	<image>In the figure, $m∠8 = 96$ and $m∠12 = 42$. Find the measure of $\angle 9$.	84
	<image>$\overline{JH}, \overline{JP},$ and $\overline{PH}$ are midsegments of $\triangle KLM$. Find $x$.	50
	<image>Find y	\frac { 5 } { 3 }
	<image>Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.	14
	<image>If $c=8,$ find $b$	4 \sqrt { 3 }
	<image>Find $m\angle T$	58
	<image>Find the area of the shaded region. Round to the nearest tenth.	68.7
	<image>Segments $\overline{AD}$ and $\overline{CE}$ are medians of $\triangle ACB, \overline{AD} \perp \overline{CE}, AB=10$, and $CE=9$. Find $CA$	\sqrt { 52 }
	<image>In $\triangle RST$, $Z$ is the centroid and $RZ=18$. Find $ZV$.	9
	<image>Find x.	45
	<image>In $\odot B$, the diameter is 20 units long, and $m \angle A C E=45$ Find $x$	\sqrt { 2 }
	<image>Find $x$.	145
	<image>Find $m \angle T$.	135
	<image>Find $x$.	7
	<image>In the figure, $m ∠ 12 = 64$. Find the measure of $ \angle 5$.	64
	<image>Triangle $CDE$ has an area of 336 square inches. Find $CE$.	28
	<image>Find $x$ in the figure.	16
	<image>Find the area of the shaded region. Round to the nearest tenth.	449.0
	<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.	259.9
	<image>Polygon ABCD ~ polygon AEFG, $m\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find the perimeter of trapezoid ABCD	73.2
	<image>In $\odot B$, $m \angle LBM = 3x$ and $m \angle LBQ = 4x + 61$. What is the measure of $\angle PBQ$?	51
	<image>Find x. Round the angle measure to the nearest degree.	40
	<image>Find $m \angle 1$.	108
	<image>Find x	22
	<image>If $m\angle ZYW = 2x - 7$ and $m \angle WYX = 2x + 5$, find $m\angle ZYW$.	39
	<image>Find $m\angle B$	90
	<image>Find $x$ in each figure.	31
	<image>Find $m \angle 6$.	45
	<image>Find x	\frac { 17 \sqrt { 2 } } { 2 }
	<image>If $FK = 3x - 1$, $KG = 4y + 3$, $JK = 6y - 2$, and $KH = 2x + 3$, find $x$ so that the quadrilateral is a parallelogram.	4
	<image>In $\odot X, A B=30, C D=30,$ and $m \widehat{C Z}=40$ Find $m\widehat{A B}$	80
	<image>Find $m \angle Q$	70
	<image>Triangle $WXY$ has an area of 248 square inches. Find the length of the base.	31
	<image>Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.	5.6
	<image>Find $m \angle 4$.	125
	<image>If WXYZ is a kite, find $YZ$	\sqrt { 89 }
	<image>Find x. Round to the nearest tenth.	5.2
	<image>Find the measure of $\angle B$	46
	<image>Find $m \angle A G E$	120
	<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.	665.1
	<image>$a=14, b=48,$ and $c=50$, find $tanB$	3.43
	<image>Find x	22.5
	<image>Find $x$.	6
	<image>Find $x$ so that the quadrilateral is a parallelogram	11
	<image>Use rhombus XYZW with $m \angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\frac{5 a+1}{4}$ Find XZ	8
	<image>Use rhombus XYZW with $m \angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\frac{5 a+1}{4}$ Find $m \angle X Y W$	53
	<image>In the figure, $QR \\| TS$, $QT \\| RS$, and $m \angle 1=131$. Find the measure of $\angle 7$.	49
	<image>Find x	8 \sqrt { 3 }
	<image>Find $x$.	25
	<image>In the figure, $ \triangle ABC$ is isosceles, $ \triangle DCE$ is equilateral, and $ \triangle FCG$ is isosceles. Find the measures of the $\angle 3$ at vertex $C$.	26
	<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.	103.9
	<image>Find y.	\frac { 3 } { 2 }

<image>Find $x$ in the figure.

90

<image>A square with side length of $9$ inches is inscribed in $\odot J$. Find the exact circumference of $\odot J$.

9 \sqrt 2 \pi

<image>Find $x$.

3

<image>If QRST is a parallelogram, find $x$

5.4

<image>For trapezoid QRST, M and P are midpoints of the legs. If TS = 2x, PM = 20, and QR = 6x, find x.

5

<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.

80

<image>Find x.

14

<image>Find $m \widehat {PO}$.

112

<image>Find the perimeter of the triangle. Round to the nearest tenth if necessary.

36

<image>Find $m\angle D$

117

<image>Points $P$, $Q$, and $R$ are the midpoints of $\overline{J K}$, $\overline{K L}$, and $\overline{J L}$, respectively. Find $x$ .

5.5

<image>Find $h$ in each triangle.

\frac { 15 \sqrt 2 } { 2 }

<image>Find $XY$.

7

<image>Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.

4.1

<image>Find the scale factor from $W$ to $W'$.

0.75

<image>Find $U B$ if $\triangle R S T \sim \triangle U V W, \overline{T A}$ and $\overline{WB}$ are medians, $T A=8$, $R A=3, W B=3 x-6,$ and $U B=x+2$

36

<image>$UJ=9, VJ=3$, and $ZT=18$. Find $JT$.

6

<image>If $MNPQ \sim XYZW,$ find the perimeter of $XYZW$.

17

<image>Find the area of the figure.

64

<image>Find x

5 \sqrt { 2 }

<image>Find $m \angle 5$.

85

<image>Quadrilateral $WXZY$ is a rhombus. If $m \angle XZY=56$, find $m \angle YWZ$.

28

<image>Find the area of the figure in feet. Round to the nearest tenth, if necessary.

14.4

<image>Find $x$.

21

<image>In $\odot P, P D=10, P Q=10,$ and $Q E=20$, find PE

10 \sqrt { 5 }

<image>If $WXYZ$ is a kite, find $ZY$.

8 \sqrt { 10 }

<image>Find the area of the regular polygon. Round to the nearest tenth.

15.6

<image>If $m \angle AFB = 8x - 6$ and $m \angle BFC = 14x + 8$, find the value of $x$ so that $\angle AFC$ is a right angle.

4

<image>Find $x$.

170

<image>Find $x$.

11.2

<image>Find the area of the figure. Round to the nearest hundredth, if necessary.

4

<image>Find the area of the figure. Round to the nearest tenth if necessary.

50

<image>Find x

24

<image>Find x.

\frac { 13 \sqrt { 2 } } { 2 }

<image>Find the measure of $\angle 1$.

56

<image>Find $y$.

3

<image>Use parallelogram ABCD to find $m\angle BCD$

52

<image>In $\odot A, m \angle E A D=42$. Find $m \widehat{C D}$

138

<image>For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.

\frac { \sqrt { 3 } } { 2 }

<image>Find x.

4 \sqrt { 13 }

<image>Find $x$. (Hint: Draw an auxiliary line.)

130

<image>Find z

2 \sqrt { 6 }

<image>In $\odot F$, find $m \widehat {AED}$.

153

<image>Find $y$ in the figure.

26.3

<image>For trapezoid $ABCD$, $S$ and $T$ are midpoints of the legs. If $AB=3x$, $ST=15$, and $CD=9x$, find $x$.

2.5

<image>If $BT = 5$ and $TC = 8$, find $CD$.

\sqrt { 89 }

<image>If $QR=2$, $XW=12$, $QW=15$, and $ST=5$, find $RS$.

8

<image>In $\odot W$, $\widehat {RS} \cong \widehat {TV}$. Find $RS$.

11

<image>In the figure, $m∠8 = 96$ and $m∠12 = 42$. Find the measure of $\angle 9$.

84

<image>$\overline{JH}, \overline{JP},$ and $\overline{PH}$ are midsegments of $\triangle KLM$. Find $x$.

50

<image>Find y

\frac { 5 } { 3 }

<image>Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.

14

<image>If $c=8,$ find $b$

4 \sqrt { 3 }

<image>Find $m\angle T$

58

<image>Find the area of the shaded region. Round to the nearest tenth.

68.7

<image>Segments $\overline{AD}$ and $\overline{CE}$ are medians of $\triangle ACB, \overline{AD} \perp \overline{CE}, AB=10$, and $CE=9$. Find $CA$

\sqrt { 52 }

<image>In $\triangle RST$, $Z$ is the centroid and $RZ=18$. Find $ZV$.

9

<image>Find x.

45

<image>In $\odot B$, the diameter is 20 units long, and $m \angle A C E=45$ Find $x$

\sqrt { 2 }

<image>Find $x$.

145

<image>Find $m \angle T$.

135

<image>Find $x$.

7

<image>In the figure, $m ∠ 12 = 64$. Find the measure of $ \angle 5$.

64

<image>Triangle $CDE$ has an area of 336 square inches. Find $CE$.

28

<image>Find $x$ in the figure.

16

<image>Find the area of the shaded region. Round to the nearest tenth.

449.0

<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.

259.9

<image>Polygon ABCD ~ polygon AEFG, $m\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find the perimeter of trapezoid ABCD

73.2

<image>In $\odot B$, $m \angle LBM = 3x$ and $m \angle LBQ = 4x + 61$. What is the measure of $\angle PBQ$?

51

<image>Find x. Round the angle measure to the nearest degree.

40

<image>Find $m \angle 1$.

108

<image>Find x

22

<image>If $m\angle ZYW = 2x - 7$ and $m \angle WYX = 2x + 5$, find $m\angle ZYW$.

39

<image>Find $m\angle B$

90

<image>Find $x$ in each figure.

31

<image>Find $m \angle 6$.

45

<image>Find x

\frac { 17 \sqrt { 2 } } { 2 }

<image>If $FK = 3x - 1$, $KG = 4y + 3$, $JK = 6y - 2$, and $KH = 2x + 3$, find $x$ so that the quadrilateral is a parallelogram.

4

<image>In $\odot X, A B=30, C D=30,$ and $m \widehat{C Z}=40$ Find $m\widehat{A B}$

80

<image>Find $m \angle Q$

70

<image>Triangle $WXY$ has an area of 248 square inches. Find the length of the base.

31

<image>Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.

5.6

<image>Find $m \angle 4$.

125

<image>If WXYZ is a kite, find $YZ$

\sqrt { 89 }

<image>Find x. Round to the nearest tenth.

5.2

<image>Find the measure of $\angle B$

46

<image>Find $m \angle A G E$

120

<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.

665.1

<image>$a=14, b=48,$ and $c=50$, find $tanB$

3.43

<image>Find x

22.5

<image>Find $x$.

6

<image>Find $x$ so that the quadrilateral is a parallelogram

11

<image>Use rhombus XYZW with $m \angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\frac{5 a+1}{4}$ Find XZ

8

<image>Use rhombus XYZW with $m \angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\frac{5 a+1}{4}$ Find $m \angle X Y W$

53

<image>In the figure, $QR \| TS$, $QT \| RS$, and $m \angle 1=131$. Find the measure of $\angle 7$.

49

<image>Find x

8 \sqrt { 3 }

<image>Find $x$.

25

<image>In the figure, $ \triangle ABC$ is isosceles, $ \triangle DCE$ is equilateral, and $ \triangle FCG$ is isosceles. Find the measures of the $\angle 3$ at vertex $C$.

26

<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.

103.9

<image>Find y.

\frac { 3 } { 2 }