hiyouga/geometry3k · Datasets at Hugging Face

images images listlengths 1 1	problem stringlengths 13 234	answer stringlengths 1 34
	<image>Find x. Round to the nearest degree.	63
	<image>Find $m \angle F$.	30
	<image>In $\triangle ABC, \overline{BD}$ is a median. If $AD=3x+5$ and $CD=5x-1,$ find $AC$.	28
	<image>WXYZ is a parallelogram. Find $m \angle X W Z$	65
	<image>In $\odot R, S U=20, Y W=20,$ and $m \widehat{Y X}=45$. Find $m\widehat{S U}$	90
	<image>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 Z	108
	<image>Find $y$ in the figure.	28
	<image>Find $y$.	1
	<image>Refer to trapezoid $CDFG$ with median $\overline{HE}$. Let $\overline{WX}$ be the median of $CDEH$. Find $WX$.	42
	<image>Find the measure of the altitude drawn to the hypotenuse	12
	<image>Find x	17.1
	<image>Find $\angle B$ of quadrilateral ABCD	90
	<image>Each pair of polygons is similar. Find y	7
	<image>Find x. Assume that any segment that appears to be tangent is tangent.	210
	<image>Find x.	\frac { 3 } { 2 } \sqrt { 3 }
	<image>$a=8, b=15,$ and $c=17$, find $sinA$	0.47
	<image>Find $y$.	11
	<image>In $\odot O, \overline{E C}$ and $\overline{A B}$ are diameters, and $\angle B O D \cong \angle D O E \cong \angle E O F \cong \angle F O A$ Find $m\widehat{B C}$	90
	<image>Find the value of $h$.	84.85
	<image>Find the measure of the altitude drawn to the hypotenuse.	\sqrt { 612 }
	<image>Find y.	7
	<image>Find x	22
	<image>Find the variable of $d$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.	16.9
	<image>Find $x$.	28
	<image>Find the area of the shaded sector. Round to the nearest tenth, if necessary.	167.1
	<image>Find the length of $FG$	39
	<image>In the figure, $\overline{A B} \parallel \overline{C E} .$ If $D A=6,$ what is $D B ?$	6
	<image>In the figure, $QR \\| TS$, $QT \\| RS$, and $m \angle 1=131$. Find the measure of $\angle 2$.	49
	<image>The area of a circle is 20 $\pi$ square centimeters. What is its circumference?	4 \sqrt 5 \pi
	<image>Find x	45
	<image>Find x.	6
	<image>Rhombus $A B C D$ is circumscribed about $\odot P$ and has a perimeter of 32 Find $x$	5
	<image>Find the area of the figure in feet. Round to the nearest tenth, if necessary.	31.2
	<image>Find $m \angle MNP$.	130
	<image>In $\odot S$, find $PR$.	12
	<image>Find x.	12
	<image>Refer to the triangle shown below. Find $z$ to the nearest tenth.	\frac { 5 } { 2 } \sqrt { 41 }
	<image>In $\triangle EFG, \overline{HL} \parallel \overline{EF}, EH=9, HG=21,$ and $FL=6 .$ Find $LG$	14
	<image>Find $x$.	3
	<image>Quadrilateral $ABDC$ is a rectangle. Find $m \angle 6$ if $ m\angle 1 = 38$.	38
	<image>Find the area of the kite.	52.5
	<image>In the figure, $ \overline{GK} \cong \overline{GH}$ and $ \overline{HK} \cong \overline{KJ}$. If $m \angle HGK=28$, find $m \angle HJK$.	38
	<image>Find AS	8
	<image>Find x. Assume that any segment that appears to be tangent is tangent.	13
	<image>Find y.	3 \sqrt { 5 }
	<image>Find the exact circumference of each circle.	5 \pi
	<image>Find $m \angle 1$.	85
	<image>The area $A$ of the shaded region is given. Find $x$. $A = 94$ in$^2$ .	55.0
	<image>Find $x$ if $\overline{PS}$ is a median of $\triangle PQR$.	2
	<image>The diameters of $\odot A, \odot B,$ and $\odot C$ are $8$ inches, $18$ inches, and $11$ inches, respectively. Find $FG$.	14
	<image>Find y.	\frac { 25 } { 14 }
	<image>If $\overline{K H}$ is parallel to $\overline{JI}$, find the measure of $\angle 2$	54
	<image>If $\overline{E B} \parallel \overline{D C},$ find $x$	9.5
	<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.	13.7
	<image>$\triangle ABC \cong \triangle FGH$. Find $x$.	3
	<image>Points $S$, $T$, and $U$ are the midpoints of $\overline{DE}$, $\overline{EF}$, and $\overline{DF}$, respectively. Find $x$.	4
	<image>Find $m \angle DBA$.	17
	<image>Circle $L$ has a radius of 32 centimeters. $\overline{L H} \perp \overline{G J},$ and $G J=40$ centimeters. Find $L K$	\sqrt { 624 }
	<image>$\triangle RST \cong \triangle VUT$. What is the area of $\triangle RST$?	300
	<image>Find x. Assume that any segment that appears to be tangent is tangent.	8
	<image>In the figure, $m∠4 = 104$, $m∠14 = 118$. Find the measure of $\angle 9$.	62
	<image>Find the area of the parallelogram.	318.7
	<image>Find $m \angle C$.	47
	<image>Find x	4 \sqrt { 3 }
	<image>$m∠4 = 32$. Find the measure of $\angle 3$.	90
	<image>If $\overline{W P}$ is a perpendicular bisector, $m \angle WHA=8 q+17$, $m \angle HWP=10+q$, $AP=6 r+4$, and $PH=22+3 r$, find $r$.	6
	<image>Find x.	5 \sqrt { 3 }
	<image>Find the measure of $RT$ of equilateral triangle $RST$ if $RS = x + 9$, $ST = 2x$, and $RT = 3x - 9$.	18
	<image>Find $m \angle 4$.	52
	<image>Find x.	10
	<image>Find the area of $▱EFGH$.	90
	<image>For trapezoid $T R S V, M$ and $N$ are midpoints of the legs. If $V S=21$ and $T R=44,$ find $M N$	32.5
	<image> $m \widehat{G H}=78$ Find $m\angle 2$	51
	<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.	6
	<image>Find $x$.	170
	<image>For the pair of similar figures, find the area of the green figure.	24
	<image>Find x.	5 \sqrt { 2 }
	<image>Find the area of the quadrilateral.	240
	<image>Find y.	10
	<image>If $\overline{GH} \cong \overline{HK}$, $\overline{HJ} \cong \overline{YK}$, and $m \angle GJK=100$, what is the measure of $\angle HGK$ ?	20
	<image>$ACDF \sim VWYZ$. Find $x$.	15
	<image>Find the angle measure of $\angle 2$.	128
	<image>ABCD is a rhombus. If EB = 9, AB = 12 and $m\angle ABD = 55$ . Find CE	\sqrt { 63 }
	<image>Find the measure of $\angle 3$.	14
	<image>Find the area of the shaded sector. Round to the nearest tenth.	46.5
	<image>$\overline{PQ}$ is tangent to circles $R$ and $S$. Find $PQ$.	4 \sqrt 6
	<image>If $SP=4, PT=6$, and $QR=12$, find $SQ$.	8
	<image>If $\overline{PQ} \cong \overline{UQ}$ and $ m ∠ P = 32 $, find $ m ∠PUQ $.	32
	<image>If CDFG is a kite, find GF	5
	<image>Find $\angle1$	112
	<image>If $x=7 \sqrt{3},$ find $y$	21 \sqrt { 3 }
	<image>Find the variable of $r$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.	1.8
	<image>Find $m \angle DH$.	162
	<image>Find $m \angle 4$.	64
	<image>Quadrilateral MNOP is a rhombus. If $m\angle PON = 124$, find $m\angle POM$.	62
	<image>Find the area of the figure. Round to the nearest tenth.	3.5
	<image>$\overline{PM}$ is a diameter of $\odot R$. Find $m \widehat {MNP}$.	180
	<image>Find x.	15.5
	<image>Find y in the figure.	5
	<image>For the pair of similar figures, use the given areas to find $x$.	10.0

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

63

<image>Find $m \angle F$.

30

<image>In $\triangle ABC, \overline{BD}$ is a median. If $AD=3x+5$ and $CD=5x-1,$ find $AC$.

28

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

65

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

90

<image>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 Z

108

<image>Find $y$ in the figure.

28

<image>Find $y$.

1

<image>Refer to trapezoid $CDFG$ with median $\overline{HE}$. Let $\overline{WX}$ be the median of $CDEH$. Find $WX$.

42

<image>Find the measure of the altitude drawn to the hypotenuse

12

<image>Find x

17.1

<image>Find $\angle B$ of quadrilateral ABCD

90

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

7

<image>Find x. Assume that any segment that appears to be tangent is tangent.

210

<image>Find x.

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

<image>$a=8, b=15,$ and $c=17$, find $sinA$

0.47

<image>Find $y$.

11

<image>In $\odot O, \overline{E C}$ and $\overline{A B}$ are diameters, and $\angle B O D \cong \angle D O E \cong \angle E O F \cong \angle F O A$ Find $m\widehat{B C}$

90

<image>Find the value of $h$.

84.85

<image>Find the measure of the altitude drawn to the hypotenuse.

\sqrt { 612 }

<image>Find y.

7

<image>Find x

22

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

16.9

<image>Find $x$.

28

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

167.1

<image>Find the length of $FG$

39

<image>In the figure, $\overline{A B} \parallel \overline{C E} .$ If $D A=6,$ what is $D B ?$

6

<image>In the figure, $QR \| TS$, $QT \| RS$, and $m \angle 1=131$. Find the measure of $\angle 2$.

49

<image>The area of a circle is 20 $\pi$ square centimeters. What is its circumference?

4 \sqrt 5 \pi

<image>Find x

45

<image>Find x.

6

<image>Rhombus $A B C D$ is circumscribed about $\odot P$ and has a perimeter of 32 Find $x$

5

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

31.2

<image>Find $m \angle MNP$.

130

<image>In $\odot S$, find $PR$.

12

<image>Find x.

12

<image>Refer to the triangle shown below. Find $z$ to the nearest tenth.

\frac { 5 } { 2 } \sqrt { 41 }

<image>In $\triangle EFG, \overline{HL} \parallel \overline{EF}, EH=9, HG=21,$ and $FL=6 .$ Find $LG$

14

<image>Find $x$.

3

<image>Quadrilateral $ABDC$ is a rectangle. Find $m \angle 6$ if $ m\angle 1 = 38$.

38

<image>Find the area of the kite.

52.5

<image>In the figure, $ \overline{GK} \cong \overline{GH}$ and $ \overline{HK} \cong \overline{KJ}$. If $m \angle HGK=28$, find $m \angle HJK$.

38

<image>Find AS

8

<image>Find x. Assume that any segment that appears to be tangent is tangent.

13

<image>Find y.

3 \sqrt { 5 }

<image>Find the exact circumference of each circle.

5 \pi

<image>Find $m \angle 1$.

85

<image>The area $A$ of the shaded region is given. Find $x$. $A = 94$ in$^2$ .

55.0

<image>Find $x$ if $\overline{PS}$ is a median of $\triangle PQR$.

2

<image>The diameters of $\odot A, \odot B,$ and $\odot C$ are $8$ inches, $18$ inches, and $11$ inches, respectively. Find $FG$.

14

<image>Find y.

\frac { 25 } { 14 }

<image>If $\overline{K H}$ is parallel to $\overline{JI}$, find the measure of $\angle 2$

54

<image>If $\overline{E B} \parallel \overline{D C},$ find $x$

9.5

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

13.7

<image>$\triangle ABC \cong \triangle FGH$. Find $x$.

3

<image>Points $S$, $T$, and $U$ are the midpoints of $\overline{DE}$, $\overline{EF}$, and $\overline{DF}$, respectively. Find $x$.

4

<image>Find $m \angle DBA$.

17

<image>Circle $L$ has a radius of 32 centimeters. $\overline{L H} \perp \overline{G J},$ and $G J=40$ centimeters. Find $L K$

\sqrt { 624 }

<image>$\triangle RST \cong \triangle VUT$. What is the area of $\triangle RST$?

300

<image>Find x. Assume that any segment that appears to be tangent is tangent.

8

<image>In the figure, $m∠4 = 104$, $m∠14 = 118$. Find the measure of $\angle 9$.

62

<image>Find the area of the parallelogram.

318.7

<image>Find $m \angle C$.

47

<image>Find x

4 \sqrt { 3 }

<image>$m∠4 = 32$. Find the measure of $\angle 3$.

90

<image>If $\overline{W P}$ is a perpendicular bisector, $m \angle WHA=8 q+17$, $m \angle HWP=10+q$, $AP=6 r+4$, and $PH=22+3 r$, find $r$.

6

<image>Find x.

5 \sqrt { 3 }

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

18

<image>Find $m \angle 4$.

52

<image>Find x.

10

<image>Find the area of $▱EFGH$.

90

<image>For trapezoid $T R S V, M$ and $N$ are midpoints of the legs. If $V S=21$ and $T R=44,$ find $M N$

32.5

<image> $m \widehat{G H}=78$ Find $m\angle 2$

51

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

6

<image>Find $x$.

170

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

24

<image>Find x.

5 \sqrt { 2 }

<image>Find the area of the quadrilateral.

240

<image>Find y.

10

<image>If $\overline{GH} \cong \overline{HK}$, $\overline{HJ} \cong \overline{YK}$, and $m \angle GJK=100$, what is the measure of $\angle HGK$ ?

20

<image>$ACDF \sim VWYZ$. Find $x$.

15

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

128

<image>ABCD is a rhombus. If EB = 9, AB = 12 and $m\angle ABD = 55$ . Find CE

\sqrt { 63 }

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

14

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

46.5

<image>$\overline{PQ}$ is tangent to circles $R$ and $S$. Find $PQ$.

4 \sqrt 6

<image>If $SP=4, PT=6$, and $QR=12$, find $SQ$.

8

<image>If $\overline{PQ} \cong \overline{UQ}$ and $ m ∠ P = 32 $, find $ m ∠PUQ $.

32

<image>If CDFG is a kite, find GF

5

<image>Find $\angle1$

112

<image>If $x=7 \sqrt{3},$ find $y$

21 \sqrt { 3 }

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

1.8

<image>Find $m \angle DH$.

162

<image>Find $m \angle 4$.

64

<image>Quadrilateral MNOP is a rhombus. If $m\angle PON = 124$, find $m\angle POM$.

62

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

3.5

<image>$\overline{PM}$ is a diameter of $\odot R$. Find $m \widehat {MNP}$.

180

<image>Find x.

15.5

<image>Find y in the figure.

5

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

10.0