Yuting6/geometry3k-white · Datasets at Hugging Face

images images listlengths 1 1	problem stringlengths 23 244	answer stringlengths 1 34
	<image>Question: The area of $▱ A B C D$ is 150 square meters. The area of $▱ F G H J$ is 54 square meters. If $▱ A B C D \sim ▱ F G H J$, find the value of $x$.	6
	<image>Question: $\overline{AB}$ is tangent to the circle. Find $x$. Round to the nearest tenth.	6.1
	<image>Question: In the figure, $m∠1 = 123$. Find the measure of $\angle 4$.	57
	<image>Question: In $\odot X, A B=30, C D=30,$ and $m \widehat{C Z}=40$ Find MB	15
	<image>Question: Find $DE$.	7.5
	<image>Question: Quadrilateral EFGH is a rectangle. If $m\angle FEG = 57$, find $m\angle GEH$.	33
	<image>Question: Find $x$.	4
	<image>Question: If $ABCD$ is a kite, find $AB$	5
	<image>Question: Find x	8
	<image>Question: Use parallelogram ABCD to find $m\angle AFB$	131
	<image>Question: If $WZ=25.3$, $YZ=22.4$, $WZ=25.3$, find $XY$.	22.4
	<image>Question: Find the value of the variable $y$ in the figure.	12
	<image>Question: In $\odot R, S U=20, Y W=20,$ and $m \widehat{Y X}=45$. Find SV	10
	<image>Question: parallelogram MNPQ with $m \angle M=10 x$ and $m \angle N=20 x$, find $\angle Q$	120
	<image>Question: Quadrilateral $RSTU$ is circumscribed about $\odot J$. If the preimeter is $18$ units, find $x$.	1.5
	<image>Question: If TR = 8, LR = 3, and RW = 6, find WS.	10
	<image>Question: Find z.	\frac { 22 } { 5 }
	<image>Question: The triangle is inscribed in $\odot D$. Find the exact circumference of $\odot D$.	4 \sqrt { 13 } \pi
	<image>Question: Find x. Round to the nearest tenth, if necessary.	5.3
	<image>Question: Find PQ	15
	<image>Question: Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.	4
	<image>Question: Find $x$.	58
	<image>Question: $\overline{RS}$ bisects $\angle VRU$. Solve for $x$.	10
	<image>Question: Find $m \angle 2$.	110
	<image>Question: Find $x$	5
	<image>Question: Find x. Assume that segments that appear to be tangent are tangent.	3.8
	<image>Question: Find $m \widehat {CF}$.	80
	<image>Question: If $b=18,$ find $c$	12 \sqrt { 3 }
	<image>Question: $\triangle FGH$ is an equilateral triangle. Find $FG$.	19
	<image>Question: Find the area of the parallelogram. Round to the nearest tenth if necessary.	259.8
	<image>Question: Find $y$ in the figure.	90
	<image>Question: If $\overline{W P}$ is a median and an angle bisector, $A P=3 y+11$, $P H=7 y-5$, $m \angle H W P=x+12$, $m \angle P A W=3 x-2$, and $m \angle H W A=4 x-16$, find $x$.	20
	<image>Question: In $\triangle JLP$, $m \angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. If $\overline{JM}$ is an altitude of $\triangle JLP$, find $x$.	32
	<image>Question: Find $\angle 7$	98
	<image>Question: Find the area of the figure. Round to the nearest hundredth, if necessary.	68.6
	<image>Question: Find z	10 \sqrt { 2 }
	<image>Question: Find x	117
	<image>Question: If PR \|\| KL, KN = 9, LN = 16, PM = 2 KP, find MR	40 / 3
	<image>Question: Find $m \angle 2$.	75
	<image>Question: Find $y$ in the figure.	11
	<image>Question: Find $m \angle 7$.	53
	<image>Question: Find the value of x.	8
	<image>Question: For the pair of similar figures, find the area of the green figure.	81
	<image>Question: The two circles are congruent. Find $x$.	16
	<image>Question: In parallelogram $ABCD$, $\overline{BD}$ and $\overline{AC}$ intersect at $E$. If $AE = 9$, $BE = 3x - 7$, and $DE = x + 5$, find $x$.	6
	<image>Question: $\overline{JH}, \overline{JP},$ and $\overline{PH}$ are midsegments of $\triangle KLM$. Find $x$.	60
	<image>Question: Find the measure of $x$.	0.5
	<image>Question: $m∠19 = 100 + 20x$, $m∠20 = 20x $. Find the measure of $\angle 19$.	140
	<image>Question: find cos B	\frac { 5 } { 7 }
	<image>Question: $\overline{XY}$ and $\overline{XZ}$ are midsegments of $\triangle RST$. Find $XZ$.	6.5
	<image>Question: Find $m\angle Z X Y$	65
	<image>Question: Find $m \angle 1$.	66
	<image>Question: Find the perimeter of the given triangle. $\triangle A B C,$ if $\triangle A B C \sim \triangle C B D, C D=4$, $D B=3,$ and $C B=5$.	20
	<image>Question: Find the perimeter of quadrilateral ABCD.	40 + 14 \sqrt { 2 }
	<image>Question: Find $y$ so that the quadrilateral is a parallelogram.	12
	<image>Question: Find $x$.	12
	<image>Question: Find DE	6
	<image>Question: $\triangle PQS \cong \triangle RQS$. Find $x$.	16
	<image>Question: Chords $\overline{A C}$ and $\overline{D F}$ are equidistant from the center. If the radius of $\odot G$ is 26 find $D E$	24
	<image>Question: Find $x$.	19
	<image>Question: Find the area of the figure. Round to the nearest tenth.	129.9
	<image>Question: Find $h$.	15 \sqrt 3
	<image>Question: Find $m\angle 2$	130
	<image>Question: Find $JL$.	12
	<image>Question: Find x. Round to the nearest tenth.	57.2
	<image>Question: isosceles trapezoid TWYZ with $\angle Z \cong \angle Y, m \angle Z=30 x$, $\angle T \cong \angle W,$ and $m \angle T=20 x$, find $\angle W$	72
	<image>Question: Express the ratio of $\tan B$ as a decimal to the nearest hundredth.	2.40
	<image>Question: Find $CB$.	15
	<image>Question: Find x.	2 \sqrt { 10 }
	<image>Question: If $\frac{I J}{X J}=\frac{HJ}{YJ}, m \angle W X J=130$, and $m \angle WZG=20,$ find $m \angle JHG$	110
	<image>Question: Quadrilateral $ABCD$ is a rhombus. If $m\angle BCD = 54$, find $m\angle BAC$.	27
	<image>Question: Polygon $BCDE$ $\cong$ polygon $RSTU$. Find $y$.	42
	<image>Question: Find the area of the parallelogram. Round to the nearest tenth if necessary.	70
	<image>Question: Find $x$.	13
	<image>Question: In the figure, $m ∠1 = 53$. Find the measure of $∠3$.	53
	<image>Question: Solve for $x$.	15
	<image>Question: Find $m\angle C$	128
	<image>Question: Find x	6
	<image>Question: Find the perimeter of the triangle. Round to the nearest hundredth.	28.52
	<image>Question: $m \widehat{G H}=78$ Find $m\angle 1$	39
	<image>Question: Quadrilateral WXYZ is a rectangle. If $XW = 3$, $WZ = 4$, and $XZ = b$, find $YW$.	5
	<image>Question: Find $y$.	2
	<image>Question: Find $z$.	10 \sqrt { 5 }
	<image>Question: Find $m\angle 2$.	151
	<image>Question: Use parallelogram to find $y$	17
	<image>Question: Find $JM$.	5.5
	<image>Question: Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.	19.2
	<image>Question: Use parallelogram WXYZ to find $m\angle WZY$	75
	<image>Question: Find the perimeter of $\triangle D E F,$ if $\triangle D E F \sim \triangle A C B$	42
	<image>Question: Find $x$.	15
	<image>Question: Find the area of the figure. Round to the nearest tenth.	474
	<image>Question: If $m \angle S=3x$ and $m \angle V=x+16$, find $m \angle S$.	24
	<image>Question: Find the value of $x$ in each diagram	52
	<image>Question: Find $BE$.	2.1
	<image>Question: Find $m \angle S$.	66
	<image>Question: Use rectangle LMNP, parallelogram LKMJ to solve the problem. If $M K=6 x, K L=3 x+2 y,$ and $J N=14-x$ find $y$	3
	<image>Question: Find $E H$ if $\triangle A B C \sim \triangle D E F, \overline{B G}$ is an altitude of $\triangle A B C, \overline{E H}$ is an altitude of $\triangle D E F, B G=3$, $B F=4, F C=2,$ and $C E=1$	\frac { 3 } { 2 }
	<image>Question: In the figure, $ m ∠1 = 3a + 40 $, $ m ∠2 = 2a + 25 $, and $ m ∠3 = 5b - 26 $. Find $b$.	27
	<image>Question: Find y	10
	<image>Question: Quadrilateral ABCD is a rectangle. $m\angle 2 = 40$. Find $m \angle 7$	40

<image>Question: The area of $▱ A B C D$ is 150 square meters. The area of $▱ F G H J$ is 54 square meters. If $▱ A B C D \sim ▱ F G H J$, find the value of $x$.

6

<image>Question: $\overline{AB}$ is tangent to the circle. Find $x$. Round to the nearest tenth.

6.1

<image>Question: In the figure, $m∠1 = 123$. Find the measure of $\angle 4$.

57

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

15

<image>Question: Find $DE$.

7.5

<image>Question: Quadrilateral EFGH is a rectangle. If $m\angle FEG = 57$, find $m\angle GEH$.

33

<image>Question: Find $x$.

4

<image>Question: If $ABCD$ is a kite, find $AB$

5

<image>Question: Find x

8

<image>Question: Use parallelogram ABCD to find $m\angle AFB$

131

<image>Question: If $WZ=25.3$, $YZ=22.4$, $WZ=25.3$, find $XY$.

22.4

<image>Question: Find the value of the variable $y$ in the figure.

12

<image>Question: In $\odot R, S U=20, Y W=20,$ and $m \widehat{Y X}=45$. Find SV

10

<image>Question: parallelogram MNPQ with $m \angle M=10 x$ and $m \angle N=20 x$, find $\angle Q$

120

<image>Question: Quadrilateral $RSTU$ is circumscribed about $\odot J$. If the preimeter is $18$ units, find $x$.

1.5

<image>Question: If TR = 8, LR = 3, and RW = 6, find WS.

10

<image>Question: Find z.

\frac { 22 } { 5 }

<image>Question: The triangle is inscribed in $\odot D$. Find the exact circumference of $\odot D$.

4 \sqrt { 13 } \pi

<image>Question: Find x. Round to the nearest tenth, if necessary.

5.3

<image>Question: Find PQ

15

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

4

<image>Question: Find $x$.

58

<image>Question: $\overline{RS}$ bisects $\angle VRU$. Solve for $x$.

10

<image>Question: Find $m \angle 2$.

110

<image>Question: Find $x$

5

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

3.8

<image>Question: Find $m \widehat {CF}$.

80

<image>Question: If $b=18,$ find $c$

12 \sqrt { 3 }

<image>Question: $\triangle FGH$ is an equilateral triangle. Find $FG$.

19

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

259.8

<image>Question: Find $y$ in the figure.

90

<image>Question: If $\overline{W P}$ is a median and an angle bisector, $A P=3 y+11$, $P H=7 y-5$, $m \angle H W P=x+12$, $m \angle P A W=3 x-2$, and $m \angle H W A=4 x-16$, find $x$.

20

<image>Question: In $\triangle JLP$, $m \angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. If $\overline{JM}$ is an altitude of $\triangle JLP$, find $x$.

32

<image>Question: Find $\angle 7$

98

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

68.6

<image>Question: Find z

10 \sqrt { 2 }

<image>Question: Find x

117

<image>Question: If PR || KL, KN = 9, LN = 16, PM = 2 KP, find MR

40 / 3

<image>Question: Find $m \angle 2$.

75

<image>Question: Find $y$ in the figure.

11

<image>Question: Find $m \angle 7$.

53

<image>Question: Find the value of x.

8

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

81

<image>Question: The two circles are congruent. Find $x$.

16

<image>Question: In parallelogram $ABCD$, $\overline{BD}$ and $\overline{AC}$ intersect at $E$. If $AE = 9$, $BE = 3x - 7$, and $DE = x + 5$, find $x$.

6

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

60

<image>Question: Find the measure of $x$.

0.5

<image>Question: $m∠19 = 100 + 20x$, $m∠20 = 20x $. Find the measure of $\angle 19$.

140

<image>Question: find cos B

\frac { 5 } { 7 }

<image>Question: $\overline{XY}$ and $\overline{XZ}$ are midsegments of $\triangle RST$. Find $XZ$.

6.5

<image>Question: Find $m\angle Z X Y$

65

<image>Question: Find $m \angle 1$.

66

<image>Question: Find the perimeter of the given triangle. $\triangle A B C,$ if $\triangle A B C \sim \triangle C B D, C D=4$, $D B=3,$ and $C B=5$.

20

<image>Question: Find the perimeter of quadrilateral ABCD.

40 + 14 \sqrt { 2 }

<image>Question: Find $y$ so that the quadrilateral is a parallelogram.

12

<image>Question: Find $x$.

12

<image>Question: Find DE

6

<image>Question: $\triangle PQS \cong \triangle RQS$. Find $x$.

16

<image>Question: Chords $\overline{A C}$ and $\overline{D F}$ are equidistant from the center. If the radius of $\odot G$ is 26 find $D E$

24

<image>Question: Find $x$.

19

<image>Question: Find the area of the figure. Round to the nearest tenth.

129.9

<image>Question: Find $h$.

15 \sqrt 3

<image>Question: Find $m\angle 2$

130

<image>Question: Find $JL$.

12

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

57.2

<image>Question: isosceles trapezoid TWYZ with $\angle Z \cong \angle Y, m \angle Z=30 x$, $\angle T \cong \angle W,$ and $m \angle T=20 x$, find $\angle W$

72

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

2.40

<image>Question: Find $CB$.

15

<image>Question: Find x.

2 \sqrt { 10 }

<image>Question: If $\frac{I J}{X J}=\frac{HJ}{YJ}, m \angle W X J=130$, and $m \angle WZG=20,$ find $m \angle JHG$

110

<image>Question: Quadrilateral $ABCD$ is a rhombus. If $m\angle BCD = 54$, find $m\angle BAC$.

27

<image>Question: Polygon $BCDE$ $\cong$ polygon $RSTU$. Find $y$.

42

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

70

<image>Question: Find $x$.

13

<image>Question: In the figure, $m ∠1 = 53$. Find the measure of $∠3$.

53

<image>Question: Solve for $x$.

15

<image>Question: Find $m\angle C$

128

<image>Question: Find x

6

<image>Question: Find the perimeter of the triangle. Round to the nearest hundredth.

28.52

<image>Question: $m \widehat{G H}=78$ Find $m\angle 1$

39

<image>Question: Quadrilateral WXYZ is a rectangle. If $XW = 3$, $WZ = 4$, and $XZ = b$, find $YW$.

5

<image>Question: Find $y$.

2

<image>Question: Find $z$.

10 \sqrt { 5 }

<image>Question: Find $m\angle 2$.

151

<image>Question: Use parallelogram to find $y$

17

<image>Question: Find $JM$.

5.5

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

19.2

<image>Question: Use parallelogram WXYZ to find $m\angle WZY$

75

<image>Question: Find the perimeter of $\triangle D E F,$ if $\triangle D E F \sim \triangle A C B$

42

<image>Question: Find $x$.

15

<image>Question: Find the area of the figure. Round to the nearest tenth.

474

<image>Question: If $m \angle S=3x$ and $m \angle V=x+16$, find $m \angle S$.

24

<image>Question: Find the value of $x$ in each diagram

52

<image>Question: Find $BE$.

2.1

<image>Question: Find $m \angle S$.

66

<image>Question: Use rectangle LMNP, parallelogram LKMJ to solve the problem. If $M K=6 x, K L=3 x+2 y,$ and $J N=14-x$ find $y$

3

<image>Question: Find $E H$ if $\triangle A B C \sim \triangle D E F, \overline{B G}$ is an altitude of $\triangle A B C, \overline{E H}$ is an altitude of $\triangle D E F, B G=3$, $B F=4, F C=2,$ and $C E=1$

\frac { 3 } { 2 }

<image>Question: In the figure, $ m ∠1 = 3a + 40 $, $ m ∠2 = 2a + 25 $, and $ m ∠3 = 5b - 26 $. Find $b$.

27

<image>Question: Find y

10

<image>Question: Quadrilateral ABCD is a rectangle. $m\angle 2 = 40$. Find $m \angle 7$

40