Yuting6/geometry3k-white · Datasets at Hugging Face

images images listlengths 1 1	problem stringlengths 23 244	answer stringlengths 1 34
	<image>Question: Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.	10
	<image>Question: Find $AC$ if $AC=x-3$, $BE=20, AB=16,$ and $CD=x+5$	32
	<image>Question: In the figure, $QR \\| TS$, $QT \\| RS$, and $m \angle 1=131$. Find the measure of $\angle 6$.	131
	<image>Question: In $\odot P, m \widehat{E N}=66$ and $m \angle G P M=89$ . Find $m \angle G N M$	44.5
	<image>Question: Find $FH$.	12
	<image>Question: If $m\angle ZXW = x - 11$ and $m \angle WZX = x - 9$, find $m\angle ZXY$.	46
	<image>Question: Find $m\angle F$	122
	<image>Question: Express the ratio of $\cos L$ as a decimal to the nearest hundredth.	0.92
	<image>Question: What is the length of $\overline{EF}$?	26
	<image>Question: Find $m \widehat {TS}$.	144
	<image>Question: Find the area of the sector. Round to the nearest tenth.	2.5
	<image>Question: In quadrilateral $P Q R S, P Q=721, Q R=547$, $R S=593, P S=756,$ and $m \angle P=58 .$ Find $m\angle R$	77.8
	<image>Question: Find $m \angle B$.	36
	<image>Question: Find the perimeter of $\triangle D E F$ if $\triangle D E F \sim \triangle A B C$	24
	<image>Question: Find $x$ so that $ m \parallel n $.	15
	<image>Question: Find the area of the quadrilateral.	104
	<image>Question: In $\triangle EDF$, $T$ is the centroid and $FT=12$. Find $TQ$.	6
	<image>Question: Find x. Assume that segments that appear to be tangent are tangent.	8
	<image>Question: If $\triangle J K L \sim \triangle P Q R$ and the area of $\triangle J K L$ is 30 square inches, find the area of $\triangle P Q R$。	46.9
	<image>Question: Find $RT$.	15
	<image>Question: Find the measure of $\angle 3$.	42
	<image>Question: $\overline{JH}$ is tangent to $\odot G$ at $J$. Find the value of $x$.	5
	<image>Question: Find $x$. $A = 177$ cm$^2$.	16.2
	<image>Question: In the figure, $QR \\| TS$, $QT \\| RS$, and $m \angle 1=131$. Find the measure of $\angle 5$.	49
	<image>Question: Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.	4
	<image>Question: In $\odot A$, $WX=XY=22$. Find $AB$.	10
	<image>Question: Find y	5 \sqrt { 2 }
	<image>Question: Find the area of the blue region.	114.2
	<image>Question: Find x. Round the side measure to the nearest tenth.	50.6
	<image>Question: Find the measure of $∠T$ to the nearest tenth.	33.7
	<image>Question: In $\odot J$, $GH=9$ and $KL=4x+1$. Find $x$.	2
	<image>Question: Find $x$ so that $m \|\| n$.	36
	<image>Question: Find the area of the figure. Round to the nearest tenth if necessary.	55.6
	<image>Question: Find x. Round to the nearest hundredth.	7.21
	<image>Question: Find $x$ so that each quadrilateral is a parallelogram.	12
	<image>Question: Find x	\frac { 50 } { 3 }
	<image>Question: The diameters of $\odot A, \odot B,$ and $\odot C$ are 10, 30 and 10 units, respectively. Find BY if $\overline{A Z} \cong \overline{C W}$ and $C W=2$.	12
	<image>Question: Find $m \angle 4$.	55
	<image>Question: Find $x$ if $\odot M \cong \odot N$.	9
	<image>Question: Find $x$ in the figure.	112
	<image>Question: Find the area of the parallelogram. Round to the nearest tenth if necessary.	39.0
	<image>Question: Find AC	9.6
	<image>Question: What is the total area of the figure?	368
	<image>Question: Find the exact circumference of the circle.	9 \pi
	<image>Question: $m$ is the perpendicular bisector of $XZ$, $WZ=4a-15$ and $WZ=a+12$. Find $WX$.	21
	<image>Question: Find the area of the triangle. Round to the nearest tenth if necessary.	96
	<image>Question: Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.	114.2
	<image>Question: In $\odot A, m \angle E A D=42$. Find $m \widehat{B C}$	42
	<image>Question: $\triangle RST \cong \triangle VUT$. Find $x$.	2
	<image>Question: In $\odot R, S U=20, Y W=20,$ and $m \widehat{Y X}=45$. Find $m\widehat{Y W}$	90
	<image>Question: Find the area of the trapezoid.	96
	<image>Question: Find y in the parallelogram	6
	<image>Question: Find $x$.	4
	<image>Question: Find $AF$.	10.8
	<image>Question: Find y.	10
	<image>Question: Two triangles are similar. Find $x$.	16.5
	<image>Question: Find $x$ so that $ m \parallel n $.	16
	<image>Question: Given right triangle $XYZ$ with hypotenuse $\overline{XY}$, $YP$ is equal to $YZ$. If $m ∠PYZ = 26$, find $m ∠XZP$.	13
	<image>Question: The segment is tangent to the circle. Find $x$.	5 \sqrt { 10 }
	<image>Question: Find $m \angle P$.	35
	<image>Question: For the pair of similar figures, use the given areas to find $x$.	6.0
	<image>Question: Find y.	\frac { 12 } { 5 } \sqrt { 11 }
	<image>Question: Find x.	\frac { 15 \sqrt { 2 } } { 2 }
	<image>Question: Find $CD$.	4
	<image>Question: Triangle $A D C$ is circumscribed about $\odot O .$ Find the perimeter of $\triangle A D C$ if $E C=D E+A F$	100
	<image>Question: Find $m \angle 5$.	57
	<image>Question: Rhombus $WXYZ$ has an area of 100 square meters. Find $WY$ if $XZ = 10$ meters.	20
	<image>Question: Find $x$.	10
	<image>Question: Find x.	13 \sqrt { 2 }
	<image>Question: Find $x$.	81.5
	<image>Question: Find $x$ so that the quadrilateral is a parallelogram.	30
	<image>Question: Find y	21
	<image>Question: Find the area of the figure. Round to the nearest tenth if necessary.	239
	<image>Question: Find the area of quadrilateral $XYZW$ if $XZ = 39$, $HW = 20$, and $YG = 21$.	799.5
	<image>Question: Find x. Assume that segments that appear to be tangent are tangent.	4
	<image>Question: In rhombus $A B C D, A B=2 x+3$ and $B C=5 x$. Find x.	1
	<image>Question: Find y.	6 \sqrt { 3 }
	<image>Question: Find the area of the kite.	72
	<image>Question: Find the value of $x$ in each diagram	93
	<image>Question: Find the measure of $\angle T$.	77
	<image>Question: In the triangle, what is the measure of $∠Z$?	18
	<image>Question: Quadrilateral ABCD is a rhombus. If $m\angle ABC = 2x – 7$ and $m\angle BCD = 2x + 3$, find $m\angle DAB$.	95
	<image>Question: The two polygons are similar. Find x.	13.5
	<image>Question: In $\triangle CDF$, $K$ is the centroid and $DK=16$. Find $KH$.	8
	<image>Question: Find $z$ in the figure.	73
	<image>Question: $\overline{PQ}$ is tangent to the circle. Find $x$. Round to the nearest tenth.	5.2
	<image>Question: Find the ratio of $MS$ to $SP$, given that $MNPQ$ is a parallelogram with $MR=\frac{1}{4} MN$	0.5
	<image>Question: Find x so that $GJ \parallel FK$. $H J=x-5, J K=15, F G=18, H G=x-4	10
	<image>Question: In $\triangle P Q R, R S=3$ and $Q S=14 .$ Find $P S$	\sqrt { 42 }
	<image>Question: JKLM is a rhombus. If $CK = 8$ and $JK = 10$, Find $JC$.	6
	<image>Question: Find x	60
	<image>Question: Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.	13
	<image>Question: Find y	\sqrt { 33 }
	<image>Question: Find the area of the shaded sector. Round to the nearest tenth.	39.3
	<image>Question: For the pair of similar figures, use the given areas to find $x$.	5
	<image>Question: Find x. Round the side measure to the nearest tenth.	107.9
	<image>Question: Equilateral pentagon $P Q R S T$ is inscribed in $\odot U$. Find $m \angle P Q R$	108
	<image>Question: If $LK=4,MP=3,PQ=6,KJ=2,RS=6$, and $LP=2$, find $QR$.	3
	<image>Question: Circle $J$ has a radius of $10$ units, $\odot K$ has a radius of $8$ units, and $BC=5.4$ units. Find $AB$.	14.6
	<image>Question: Find the measure of $∠R$ to the nearest tenth.	70.9

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

10

<image>Question: Find $AC$ if $AC=x-3$, $BE=20, AB=16,$ and $CD=x+5$

32

<image>Question: In the figure, $QR \| TS$, $QT \| RS$, and $m \angle 1=131$. Find the measure of $\angle 6$.

131

<image>Question: In $\odot P, m \widehat{E N}=66$ and $m \angle G P M=89$ . Find $m \angle G N M$

44.5

<image>Question: Find $FH$.

12

<image>Question: If $m\angle ZXW = x - 11$ and $m \angle WZX = x - 9$, find $m\angle ZXY$.

46

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

122

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

0.92

<image>Question: What is the length of $\overline{EF}$?

26

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

144

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

2.5

<image>Question: In quadrilateral $P Q R S, P Q=721, Q R=547$, $R S=593, P S=756,$ and $m \angle P=58 .$ Find $m\angle R$

77.8

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

36

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

24

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

15

<image>Question: Find the area of the quadrilateral.

104

<image>Question: In $\triangle EDF$, $T$ is the centroid and $FT=12$. Find $TQ$.

6

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

8

<image>Question: If $\triangle J K L \sim \triangle P Q R$ and the area of $\triangle J K L$ is 30 square inches, find the area of $\triangle P Q R$。

46.9

<image>Question: Find $RT$.

15

<image>Question: Find the measure of $\angle 3$.

42

<image>Question: $\overline{JH}$ is tangent to $\odot G$ at $J$. Find the value of $x$.

5

<image>Question: Find $x$. $A = 177$ cm$^2$.

16.2

<image>Question: In the figure, $QR \| TS$, $QT \| RS$, and $m \angle 1=131$. Find the measure of $\angle 5$.

49

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

4

<image>Question: In $\odot A$, $WX=XY=22$. Find $AB$.

10

<image>Question: Find y

5 \sqrt { 2 }

<image>Question: Find the area of the blue region.

114.2

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

50.6

<image>Question: Find the measure of $∠T$ to the nearest tenth.

33.7

<image>Question: In $\odot J$, $GH=9$ and $KL=4x+1$. Find $x$.

2

<image>Question: Find $x$ so that $m || n$.

36

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

55.6

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

7.21

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

12

<image>Question: Find x

\frac { 50 } { 3 }

<image>Question: The diameters of $\odot A, \odot B,$ and $\odot C$ are 10, 30 and 10 units, respectively. Find BY if $\overline{A Z} \cong \overline{C W}$ and $C W=2$.

12

<image>Question: Find $m \angle 4$.

55

<image>Question: Find $x$ if $\odot M \cong \odot N$.

9

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

112

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

39.0

<image>Question: Find AC

9.6

<image>Question: What is the total area of the figure?

368

<image>Question: Find the exact circumference of the circle.

9 \pi

<image>Question: $m$ is the perpendicular bisector of $XZ$, $WZ=4a-15$ and $WZ=a+12$. Find $WX$.

21

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

96

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

114.2

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

42

<image>Question: $\triangle RST \cong \triangle VUT$. Find $x$.

2

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

90

<image>Question: Find the area of the trapezoid.

96

<image>Question: Find y in the parallelogram

6

<image>Question: Find $x$.

4

<image>Question: Find $AF$.

10.8

<image>Question: Find y.

10

<image>Question: Two triangles are similar. Find $x$.

16.5

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

16

<image>Question: Given right triangle $XYZ$ with hypotenuse $\overline{XY}$, $YP$ is equal to $YZ$. If $m ∠PYZ = 26$, find $m ∠XZP$.

13

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

5 \sqrt { 10 }

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

35

<image>Question: For the pair of similar figures, use the given areas to find $x$.

6.0

<image>Question: Find y.

\frac { 12 } { 5 } \sqrt { 11 }

<image>Question: Find x.

\frac { 15 \sqrt { 2 } } { 2 }

<image>Question: Find $CD$.

4

<image>Question: Triangle $A D C$ is circumscribed about $\odot O .$ Find the perimeter of $\triangle A D C$ if $E C=D E+A F$

100

<image>Question: Find $m \angle 5$.

57

<image>Question: Rhombus $WXYZ$ has an area of 100 square meters. Find $WY$ if $XZ = 10$ meters.

20

<image>Question: Find $x$.

10

<image>Question: Find x.

13 \sqrt { 2 }

<image>Question: Find $x$.

81.5

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

30

<image>Question: Find y

21

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

239

<image>Question: Find the area of quadrilateral $XYZW$ if $XZ = 39$, $HW = 20$, and $YG = 21$.

799.5

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

4

<image>Question: In rhombus $A B C D, A B=2 x+3$ and $B C=5 x$. Find x.

1

<image>Question: Find y.

6 \sqrt { 3 }

<image>Question: Find the area of the kite.

72

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

93

<image>Question: Find the measure of $\angle T$.

77

<image>Question: In the triangle, what is the measure of $∠Z$?

18

<image>Question: Quadrilateral ABCD is a rhombus. If $m\angle ABC = 2x – 7$ and $m\angle BCD = 2x + 3$, find $m\angle DAB$.

95

<image>Question: The two polygons are similar. Find x.

13.5

<image>Question: In $\triangle CDF$, $K$ is the centroid and $DK=16$. Find $KH$.

8

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

73

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

5.2

<image>Question: Find the ratio of $MS$ to $SP$, given that $MNPQ$ is a parallelogram with $MR=\frac{1}{4} MN$

0.5

<image>Question: Find x so that $GJ \parallel FK$. $H J=x-5, J K=15, F G=18, H G=x-4

10

<image>Question: In $\triangle P Q R, R S=3$ and $Q S=14 .$ Find $P S$

\sqrt { 42 }

<image>Question: JKLM is a rhombus. If $CK = 8$ and $JK = 10$, Find $JC$.

6

<image>Question: Find x

60

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

13

<image>Question: Find y

\sqrt { 33 }

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

39.3

<image>Question: For the pair of similar figures, use the given areas to find $x$.

5

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

107.9

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

108

<image>Question: If $LK=4,MP=3,PQ=6,KJ=2,RS=6$, and $LP=2$, find $QR$.

3

<image>Question: Circle $J$ has a radius of $10$ units, $\odot K$ has a radius of $8$ units, and $BC=5.4$ units. Find $AB$.

14.6

<image>Question: Find the measure of $∠R$ to the nearest tenth.

70.9