hiyouga/geometry3k · Datasets at Hugging Face

images images listlengths 1 1	problem stringlengths 13 234	answer stringlengths 1 34
	<image>Find $x$.	2
	<image>In $\odot F$, $GK=14$ and $m \widehat{GHK}=142$. Find $m \widehat {KM}$.	109
	<image>Find x. Round the side measure to the nearest tenth.	8.3
	<image>Find the perimeter of the triangle.	100.4
	<image>Find x.	3 \sqrt { 29 }
	<image>Each pair of polygons is similar. Find CE	11.4
	<image>Find $RS$.	31
	<image>Find the value of $s$ in the parallelogram.	13
	<image>Find x.	12.0
	<image>For the pair of similar figures, find the area of the green figure.	12.5
	<image>Find x. Round side measures to the nearest tenth.	35.1
	<image>Find $x$ if $\triangle JMN$ is an isosceles triangle with $\overline{JM} \cong \overline{M N}$.	4
	<image>Find x	39.8
	<image>$\Delta DFG$ and $\Delta F G H$ are isosceles, $m \angle FDH=28$ and$\overline{DG} \cong \overline{FG} \cong \overline{FH}$. Find the measure of $\angle DFG$.	28
	<image>Use parallelogram to find $x$	79
	<image>If $\overline{TU} \perp \overline{UV}$ and $\overline{UV} \perp \overline{VW}$, find $m \angle 1$.	45
	<image>If $\angle R S T$ is a right angle, $\overline{SU} \perp \overline{RT}$, $\overline{UV} \perp \overline{ST},$ and $m \angle RT S=47,$ find $m \angle SUV$	47
	<image>Find the area of the shaded sector. Round to the nearest tenth.	10.0
	<image>Find $x$ so that the quadrilateral is a parallelogram.	4
	<image>Find x.	6 \sqrt { 2 }
	<image>Find $m \widehat {GJF}$.	196
	<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.	4
	<image>$P$ is the incenter of $\triangle AEC$. Find $DE$. Rounded to the nearest hundredth.	13.11
	<image>Express the ratio of $\tan X$ as a decimal to the nearest hundredth.	3.43
	<image>Find $x$.	3
	<image>Use parallelogram to find $a$	2
	<image>The segment is tangent to the circle. Find $x$.	4
	<image>Find the area of the shaded region. Round to the nearest tenth.	61.7
	<image>The segment is tangent to the circle. Find $x$ to the nearest hundredth.	8.06
	<image>Find x.	20
	<image>Find $x$.	11
	<image>Find the perimeter of the figure.	36
	<image>Find the exact value of $DE,$ given $AD=12$ and $BD=4$	2 \sqrt { 3 }
	<image>In the figure, $m∠3 = 43$. Find the measure of $\angle 16$.	137
	<image>Find $JK$.	12
	<image>In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\angle 4$.	62
	<image>WXYZ is a parallelogram. Find $m \angle Y Z W$	115
	<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.	727.5
	<image>Find the area of the quadrilateral.	260
	<image>Find x	12
	<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.	60.1
	<image>Find x.	12
	<image>Find $m \angle TQR$.	43
	<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.	8
	<image>Quadrilateral $ABCD$ is a rhombus. If $AB = 14$, find $BC$.	14
	<image>Find the measure of $\angle 2$ if $m∠4= m∠5$.	53
	<image>Find x. Round the side measure to the nearest tenth.	6.1
	<image>For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.	\frac { 3 } { 7 }
	<image>Find x.	6
	<image>Find $y$.	2
	<image>Find the measure of $ST$ of equilateral triangle $RST$ if $RS = x + 9$, $ST = 2x$, and $RT = 3x - 9$.	18
	<image>Use parallelogram NQRM to find QR	15
	<image>Equilateral pentagon $P Q R S T$ is inscribed in $\odot U$. Find $m \angle P T S$	144
	<image>In $\odot X, A B=30, C D=30,$ and $m \widehat{C Z}=40$ Find AM	15
	<image>Use parallelogram ABCD to find $x$	5
	<image>Find $x$ so that $ m \parallel n $.	9
	<image>Find $x$ so that each quadrilateral is a parallelogram.	8
	<image>If $a=10 \sqrt{3},$ find $C E$	15
	<image>Find the measure of $\angle 4$ if $m \angle D G F=53$ and $m \angle A G C=40$.	40
	<image>Polygon $BCDE$ $\cong$ polygon $RSTU$. Find $w$.	10
	<image>If $\overline{K H}$ is parallel to $\overline{JI}$, find the measure of $\angle 1$	66
	<image>Each pair of polygons is similar. Find x	10
	<image>Find x. Round to the nearest tenth.	7.1
	<image>Find $m \angle 3$.	68
	<image>Find $JL$, if $KP = 4$ and $PM = 7$	11
	<image>Find $x$ so that each quadrilateral is a parallelogram.	6
	<image>Find x.	9 \sqrt { 3 }
	<image>Use parallelogram PQRS to find $m\angle R$	52
	<image>Find $x$.	102
	<image>Find $AB$.	10
	<image>$ABCD \sim QSRP$. Find $x$.	63
	<image>The two polygons are similar. Then find y.	20.5
	<image>Solve for $x$.	6
	<image>Find x	5 \sqrt { 2 }
	<image>In the figure, a regular polygon is inscribed in a circle. Find the measure of a central angle.	72
	<image>Find the perimeter of the figure. Round to the nearest tenth if necessary.	31.4
	<image>Find the measure of $\angle 2$ in the figure.	105
	<image>Find the area of the shaded sector. Round to the nearest tenth, if necessary.	322.0
	<image>Quadrilateral $WXYZ$ is a rectangle. Find the measure of $\angle 12$ if $m∠1 = 30$.	120
	<image>Find x. Assume that segments that appear to be tangent are tangent.	6
	<image>$RP=3.5$ and $JP=9$. Find $PS$.	4.5
	<image>Polygon $BCDE$ $\cong$ polygon $RSTU$. Find $z$.	3
	<image>Find z.	8
	<image>In the figure, $m∠1 = 123$. Find the measure of $\angle 16$.	57
	<image>In $\triangle JLP$, $m \angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. Find $LK$ if $\overline{PK}$ is a median.	7
	<image>Given figure $A B C D$, with $\overline{A B} \\| \overline{D C}, m \angle B=60, m \angle D=45, B C=8$ and $A B=24,$ find the perimeter.	52 + 4 \sqrt { 3 } + 4 \sqrt { 6 }
	<image>For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.	\frac { 5 } { 6 }
	<image>Find $x$.	5
	<image>Circle $W$ has a radius of 4 units, $\odot Z$ has a radius of 7 units, and $X Y=2 .$ Find $Y Z$	5
	<image>Find $y$.	3
	<image>Find $m\angle 3$.	12
	<image>Find x	4 \sqrt { 29 }
	<image>$ABCD \sim QSRP$. Find $y$.	32
	<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.	22.7
	<image>Find $x$.	114
	<image>In the figure, $m ∠9 = 75$. Find the measure of $\angle 8$.	105
	<image>In H, the diameter is $18$, $LM = 12$, and $m \widehat {LM} = 84$. Find $m \widehat {LK}$.	42
	<image>Find x	42.5
	<image>Find $m \angle H$.	54
	<image>Find $h$.	4 \sqrt 2

<image>Find $x$.

2

<image>In $\odot F$, $GK=14$ and $m \widehat{GHK}=142$. Find $m \widehat {KM}$.

109

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

8.3

<image>Find the perimeter of the triangle.

100.4

<image>Find x.

3 \sqrt { 29 }

<image>Each pair of polygons is similar. Find CE

11.4

<image>Find $RS$.

31

<image>Find the value of $s$ in the parallelogram.

13

<image>Find x.

12.0

<image>For the pair of similar figures, find the area of the green figure.

12.5

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

35.1

<image>Find $x$ if $\triangle JMN$ is an isosceles triangle with $\overline{JM} \cong \overline{M N}$.

4

<image>Find x

39.8

<image>$\Delta DFG$ and $\Delta F G H$ are isosceles, $m \angle FDH=28$ and$\overline{DG} \cong \overline{FG} \cong \overline{FH}$. Find the measure of $\angle DFG$.

28

<image>Use parallelogram to find $x$

79

<image>If $\overline{TU} \perp \overline{UV}$ and $\overline{UV} \perp \overline{VW}$, find $m \angle 1$.

45

<image>If $\angle R S T$ is a right angle, $\overline{SU} \perp \overline{RT}$, $\overline{UV} \perp \overline{ST},$ and $m \angle RT S=47,$ find $m \angle SUV$

47

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

10.0

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

4

<image>Find x.

6 \sqrt { 2 }

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

196

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

4

<image>$P$ is the incenter of $\triangle AEC$. Find $DE$. Rounded to the nearest hundredth.

13.11

<image>Express the ratio of $\tan X$ as a decimal to the nearest hundredth.

3.43

<image>Find $x$.

3

<image>Use parallelogram to find $a$

2

<image>The segment is tangent to the circle. Find $x$.

4

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

61.7

<image>The segment is tangent to the circle. Find $x$ to the nearest hundredth.

8.06

<image>Find x.

20

<image>Find $x$.

11

<image>Find the perimeter of the figure.

36

<image>Find the exact value of $DE,$ given $AD=12$ and $BD=4$

2 \sqrt { 3 }

<image>In the figure, $m∠3 = 43$. Find the measure of $\angle 16$.

137

<image>Find $JK$.

12

<image>In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\angle 4$.

62

<image>WXYZ is a parallelogram. Find $m \angle Y Z W$

115

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

727.5

<image>Find the area of the quadrilateral.

260

<image>Find x

12

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

60.1

<image>Find x.

12

<image>Find $m \angle TQR$.

43

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

8

<image>Quadrilateral $ABCD$ is a rhombus. If $AB = 14$, find $BC$.

14

<image>Find the measure of $\angle 2$ if $m∠4= m∠5$.

53

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

6.1

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

\frac { 3 } { 7 }

<image>Find x.

6

<image>Find $y$.

2

<image>Find the measure of $ST$ of equilateral triangle $RST$ if $RS = x + 9$, $ST = 2x$, and $RT = 3x - 9$.

18

<image>Use parallelogram NQRM to find QR

15

<image>Equilateral pentagon $P Q R S T$ is inscribed in $\odot U$. Find $m \angle P T S$

144

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

15

<image>Use parallelogram ABCD to find $x$

5

<image>Find $x$ so that $ m \parallel n $.

9

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

8

<image>If $a=10 \sqrt{3},$ find $C E$

15

<image>Find the measure of $\angle 4$ if $m \angle D G F=53$ and $m \angle A G C=40$.

40

<image>Polygon $BCDE$ $\cong$ polygon $RSTU$. Find $w$.

10

<image>If $\overline{K H}$ is parallel to $\overline{JI}$, find the measure of $\angle 1$

66

<image>Each pair of polygons is similar. Find x

10

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

7.1

<image>Find $m \angle 3$.

68

<image>Find $JL$, if $KP = 4$ and $PM = 7$

11

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

6

<image>Find x.

9 \sqrt { 3 }

<image>Use parallelogram PQRS to find $m\angle R$

52

<image>Find $x$.

102

<image>Find $AB$.

10

<image>$ABCD \sim QSRP$. Find $x$.

63

<image>The two polygons are similar. Then find y.

20.5

<image>Solve for $x$.

6

<image>Find x

5 \sqrt { 2 }

<image>In the figure, a regular polygon is inscribed in a circle. Find the measure of a central angle.

72

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

31.4

<image>Find the measure of $\angle 2$ in the figure.

105

<image>Find the area of the shaded sector. Round to the nearest tenth, if necessary.

322.0

<image>Quadrilateral $WXYZ$ is a rectangle. Find the measure of $\angle 12$ if $m∠1 = 30$.

120

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

6

<image>$RP=3.5$ and $JP=9$. Find $PS$.

4.5

<image>Polygon $BCDE$ $\cong$ polygon $RSTU$. Find $z$.

3

<image>Find z.

8

<image>In the figure, $m∠1 = 123$. Find the measure of $\angle 16$.

57

<image>In $\triangle JLP$, $m \angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. Find $LK$ if $\overline{PK}$ is a median.

7

<image>Given figure $A B C D$, with $\overline{A B} \| \overline{D C}, m \angle B=60, m \angle D=45, B C=8$ and $A B=24,$ find the perimeter.

52 + 4 \sqrt { 3 } + 4 \sqrt { 6 }

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

\frac { 5 } { 6 }

<image>Find $x$.

5

<image>Circle $W$ has a radius of 4 units, $\odot Z$ has a radius of 7 units, and $X Y=2 .$ Find $Y Z$

5

<image>Find $y$.

3

<image>Find $m\angle 3$.

12

<image>Find x

4 \sqrt { 29 }

<image>$ABCD \sim QSRP$. Find $y$.

32

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

22.7

<image>Find $x$.

114

<image>In the figure, $m ∠9 = 75$. Find the measure of $\angle 8$.

105

<image>In H, the diameter is $18$, $LM = 12$, and $m \widehat {LM} = 84$. Find $m \widehat {LK}$.

42

<image>Find x

42.5

<image>Find $m \angle H$.

54

<image>Find $h$.

4 \sqrt 2