Yuting6/geoqa-r1v-8k-mixup · Datasets at Hugging Face

images images listlengths 1 1	problem stringlengths 16 729	answer stringlengths 8 30
	<image>Question: \triangle A B C \cong \triangle F G H. Find x.	\boxed{3}
	<image>Question: If x = 7 \sqrt { 3 }, find y.	\boxed{21\sqrt{3}}
	<image>Question: Find m \angle H.	\boxed{54}
	<image>Question: Find the measure of \angle T to the nearest tenth.	\boxed{56.4}
	<image>Question: Use parallelogram J K L M to find m \angle J M L if J K = 2 b + 3 and J M = 3 a.	\boxed{80}
	<image>Question: Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.	\boxed{4}
	<image>Question: If 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.	\boxed{20}
	<image>Question: Find y if \triangle J L M \sim \triangle Q S T.	\boxed{4}
	<image>Question: Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.	\boxed{6}
	<image>Question: Find x so that the quadrilateral is a parallelogram.	\boxed{2}
	<image>Question: Find m \angle 5.	\boxed{110}
	<image>Question: find \cos S.	\boxed{0.8}
	<image>Question: Find B D.	\boxed{1.8}
	<image>Question: If Q R = 2, X W = 12, Q W = 15, and S T = 5, find W V.	\boxed{7.5}
	<image>Question: Find x.	\boxed{10}
	<image>Question: Find m \angle 5.	\boxed{55}
	<image>Question: Find m \angle W.	\boxed{74}
	<image>Question: Find T R.	\boxed{4}
	<image>Question: Equilateral pentagon P Q R S T is inscribed in \odot U. Find m \angle P Q R.	\boxed{108}
	<image>Question: Find the measure of \angle 8 if A B \perp B C.	\boxed{14}
	<image>Question: Find x.	\boxed{28.2}
	<image>Question: Find x. Round the side measure to the nearest tenth.	\boxed{14.9}
	<image>Question: Find x to the nearest tenth.	\boxed{150}
	<image>Question: Find m \angle 3.	\boxed{55}
	<image>Question: Find x. Round the angle measure to the nearest degree.	\boxed{48}
	<image>Question: Find A X if E X = 24 and D E = 7.	\boxed{24}
	<image>Question: In the figure, m \angle 3 = 43. Find the measure of \angle 7.	\boxed{43}
	<image>Question: Find R T.	\boxed{8}
	<image>Question: The diagonals of rectangle A B C D the have a length of 56 feet. If m \angle B A C = 42, what is the length of A B to the nearest tenth of a foot?	\boxed{41.6}
	<image>Question: Find the area of the shaded region. Round to the nearest tenth.	\boxed{68.7}
	<image>Question: Find m \angle Y.	\boxed{60}
	<image>Question: Find the perimeter of the \triangle A B C, if \triangle A B C \sim \triangle C B D, A D = 5, C D = 12, and B C = 31.2.	\boxed{78}
	<image>Question: Find the area of the quadrilateral.	\boxed{260}
	<image>Question: Find x. A = 92 in^2.	\boxed{8.4}
	<image>Question: If W Z = 25.3, Y Z = 22.4, W Z = 25.3, find X Y.	\boxed{22.4}
	<image>Question: Find y so that the quadrilateral is a parallelogram.	\boxed{12}
	<image>Question: Find x.	\boxed{27}
	<image>Question: If x = 7 \sqrt { 3 }, find b.	\boxed{42}
	<image>Question: isosceles trapezoid T W Y Z with \angle Z \cong \angle Y, m \angle Z = 30 x, \angle T \cong \angle W, and m \angle T = 20 x, find Z.	\boxed{108}
	<image>Question: Find the area of the triangle. Round to the nearest tenth if necessary.	\boxed{6}
	<image>Question: Find x. Round to the nearest hundredth.	\boxed{16.93}
	<image>Question: Find the area of the figure. Round to the nearest tenth if necessary.	\boxed{3108}
	<image>Question: Use a calculator to find the measure of \angle J to the nearest degree.	\boxed{45}
	<image>Question: Find y.	\boxed{10\sqrt{3}}
	<image>Question: Quadrilateral W X Y Z is a rectangle. Find the measure of \angle 8 if m \angle 1 = 30.	\boxed{30}
	<image>Question: Find the measure of \angle R.	\boxed{122}
	<image>Question: Rhombus A B C D is circumscribed about \odot P and has a perimeter of 32. Find x.	\boxed{5}
	<image>Question: Find the measure of \angle 1 in the figure.	\boxed{80}
	<image>Question: \triangle R S T \cong \triangle V U T. Find x.	\boxed{2}
	<image>Question: Find m \angle 2.	\boxed{23}
	<image>Question: Find m \angle G.	\boxed{93}
	<image>Question: W X Y Z is a parallelogram. Find m \angle Y Z W.	\boxed{115}
	<image>Question: Find the area of the figure. Round to the nearest tenth if necessary.	\boxed{408}
	<image>Question: Find \sin x.	\boxed{\frac{2\sqrt{2}}{5}}
	<image>Question: Find y.	\boxed{9.6\sqrt{2}}
	<image>Question: Find the measure of \angle 3 in the figure.	\boxed{25}
	<image>Question: Rhombus Q R S T has an area of 137.9 square meters. If R T is 12.2 meters, find Q S.	\boxed{22.6}
	<image>Question: Find the measure of X T.	\boxed{7}
	<image>Question: Find x. A = 96 in^2.	\boxed{6.6}
	<image>Question: Find m \widehat G J F.	\boxed{196}
	<image>Question: In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 5.	\boxed{60}
	<image>Question: In \odot G, m \angle A G B = 30 and C G \perp G D. Find m \widehat F D.	\boxed{30}
	<image>Question: In the figure, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 10.	\boxed{55}
	<image>Question: In the figure, m \angle 3 = 43. Find the measure of \angle 2.	\boxed{137}
	<image>Question: What is the total area of the figure?	\boxed{368}
	<image>Question: Use parallelogram to find a.	\boxed{7}
	<image>Question: If A D = 27, A B = 8, and A E = 12, find B C.	\boxed{10}
	<image>Question: The diameters of \odot A, \odot B, and \odot C are 8 inches, 18 inches, and 11 inches, respectively. Find F B.	\boxed{5}
	<image>Question: Find the ratio of M S to S P, given that M N P Q is a parallelogram with M R = \frac { 1 } { 4 } M N.	\boxed{0.5}
	<image>Question: Find x.	\boxed{2\sqrt{22}}
	<image>Question: Find z.	\boxed{10\sqrt{2}}
	<image>Question: Find m \angle Z in the trapezoid.	\boxed{68}
	<image>Question: Find x.	\boxed{8\sqrt{2}}
	<image>Question: In the figure, m \angle 2 = 110 and m \angle 12 = 55. Find the measure of \angle 2.	\boxed{70}
	<image>Question: Find m \angle 1.	\boxed{55}
	<image>Question: Find x.	\boxed{2\sqrt{10}}
	<image>Question: Find the area of the figure. Round to the nearest tenth if necessary.	\boxed{164.3}
	<image>Question: Find the perimeter of the \triangle D E F, if \triangle D E F \sim \triangle C B F, perimeter of \triangle C B F = 27, D F = 6, F C = 8.	\boxed{20.25}
	<image>Question: In quadrilateral A B C D, A C = 188, B D = 214, m \angle B P C = 70, and P is the midpoint of A C and B D. Find the perimeter of quadrilateral A B C D.	\boxed{561.2}
	<image>Question: a = 8, b = 15, and c = 17, find \cos B.	\boxed{0.47}
	<image>Question: Use parallelogram A B C D to find m \angle B D C.	\boxed{87.9}
	<image>Question: What is the value of \tan x?	\boxed{\frac{5}{12}}
	<image>Question: Find y.	\boxed{6\sqrt{42}}
	<image>Question: Find y.	\boxed{32.6}
	<image>Question: Find x. A = 153 in^2.	\boxed{17}
	<image>Question: Find m \angle A B D.	\boxed{103}
	<image>Question: Find x.	\boxed{4\sqrt{3}}
	<image>Question: Find x.	\boxed{2\sqrt{21}}
	<image>Question: Find the value of x in the diagram.	\boxed{20}
	<image>Question: Find y so that the quadrilateral is a parallelogram.	\boxed{16}
	<image>Question: In the figure, m \angle 12 = 64. Find the measure of \angle 8.	\boxed{116}
	<image>Question: A square with side length of 9 inches is inscribed in \odot J. Find the exact circumference of \odot J.	\boxed{9\sqrt2\pi}
	<image>Question: In the figure, the vertices of quadrilateral A B C D intersect square E F G H and divide its sides into segments with measure that have a ratio of 1:2. Find the area of A B C D.	\boxed{45}
	<image>Question: Find x. Assume that segments that appear to be tangent are tangent.	\boxed{8}
	<image>Question: Triangle W X Y has an area of 248 square inches. Find the length of the base.	\boxed{31}
	<image>Question: Find x. Round the side measure to the nearest tenth.	\boxed{34.8}
	<image>Question: Use the figure to find the indicated variable. Find y if m \angle 3 = 4 y + 30 and m \angle 7 = 7 y + 6.	\boxed{8}
	<image>Question: Find m \angle 3.	\boxed{95}
	<image>Question: Use parallelogram A B C D to find C D.	\boxed{6}
	<image>Question: Find m \angle T.	\boxed{46}

<image>Question: \triangle A B C \cong \triangle F G H. Find x.

\boxed{3}

<image>Question: If x = 7 \sqrt { 3 }, find y.

\boxed{21\sqrt{3}}

<image>Question: Find m \angle H.

\boxed{54}

<image>Question: Find the measure of \angle T to the nearest tenth.

\boxed{56.4}

<image>Question: Use parallelogram J K L M to find m \angle J M L if J K = 2 b + 3 and J M = 3 a.

\boxed{80}

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

\boxed{4}

<image>Question: If 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.

\boxed{20}

<image>Question: Find y if \triangle J L M \sim \triangle Q S T.

\boxed{4}

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

\boxed{6}

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

\boxed{2}

<image>Question: Find m \angle 5.

\boxed{110}

<image>Question: find \cos S.

\boxed{0.8}

<image>Question: Find B D.

\boxed{1.8}

<image>Question: If Q R = 2, X W = 12, Q W = 15, and S T = 5, find W V.

\boxed{7.5}

<image>Question: Find x.

\boxed{10}

<image>Question: Find m \angle 5.

\boxed{55}

<image>Question: Find m \angle W.

\boxed{74}

<image>Question: Find T R.

\boxed{4}

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

\boxed{108}

<image>Question: Find the measure of \angle 8 if A B \perp B C.

\boxed{14}

<image>Question: Find x.

\boxed{28.2}

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

\boxed{14.9}

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

\boxed{150}

<image>Question: Find m \angle 3.

\boxed{55}

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

\boxed{48}

<image>Question: Find A X if E X = 24 and D E = 7.

\boxed{24}

<image>Question: In the figure, m \angle 3 = 43. Find the measure of \angle 7.

\boxed{43}

<image>Question: Find R T.

\boxed{8}

<image>Question: The diagonals of rectangle A B C D the have a length of 56 feet. If m \angle B A C = 42, what is the length of A B to the nearest tenth of a foot?

\boxed{41.6}

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

\boxed{68.7}

<image>Question: Find m \angle Y.

\boxed{60}

<image>Question: Find the perimeter of the \triangle A B C, if \triangle A B C \sim \triangle C B D, A D = 5, C D = 12, and B C = 31.2.

\boxed{78}

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

\boxed{260}

<image>Question: Find x. A = 92 in^2.

\boxed{8.4}

<image>Question: If W Z = 25.3, Y Z = 22.4, W Z = 25.3, find X Y.

\boxed{22.4}

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

\boxed{12}

<image>Question: Find x.

\boxed{27}

<image>Question: If x = 7 \sqrt { 3 }, find b.

\boxed{42}

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

\boxed{108}

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

\boxed{6}

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

\boxed{16.93}

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

\boxed{3108}

<image>Question: Use a calculator to find the measure of \angle J to the nearest degree.

\boxed{45}

<image>Question: Find y.

\boxed{10\sqrt{3}}

<image>Question: Quadrilateral W X Y Z is a rectangle. Find the measure of \angle 8 if m \angle 1 = 30.

\boxed{30}

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

\boxed{122}

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

\boxed{5}

<image>Question: Find the measure of \angle 1 in the figure.

\boxed{80}

<image>Question: \triangle R S T \cong \triangle V U T. Find x.

\boxed{2}

<image>Question: Find m \angle 2.

\boxed{23}

<image>Question: Find m \angle G.

\boxed{93}

<image>Question: W X Y Z is a parallelogram. Find m \angle Y Z W.

\boxed{115}

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

\boxed{408}

<image>Question: Find \sin x.

\boxed{\frac{2\sqrt{2}}{5}}

<image>Question: Find y.

\boxed{9.6\sqrt{2}}

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

\boxed{25}

<image>Question: Rhombus Q R S T has an area of 137.9 square meters. If R T is 12.2 meters, find Q S.

\boxed{22.6}

<image>Question: Find the measure of X T.

\boxed{7}

<image>Question: Find x. A = 96 in^2.

\boxed{6.6}

<image>Question: Find m \widehat G J F.

\boxed{196}

<image>Question: In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 5.

\boxed{60}

<image>Question: In \odot G, m \angle A G B = 30 and C G \perp G D. Find m \widehat F D.

\boxed{30}

<image>Question: In the figure, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 10.

\boxed{55}

<image>Question: In the figure, m \angle 3 = 43. Find the measure of \angle 2.

\boxed{137}

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

\boxed{368}

<image>Question: Use parallelogram to find a.

\boxed{7}

<image>Question: If A D = 27, A B = 8, and A E = 12, find B C.

\boxed{10}

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

\boxed{5}

<image>Question: Find the ratio of M S to S P, given that M N P Q is a parallelogram with M R = \frac { 1 } { 4 } M N.

\boxed{0.5}

<image>Question: Find x.

\boxed{2\sqrt{22}}

<image>Question: Find z.

\boxed{10\sqrt{2}}

<image>Question: Find m \angle Z in the trapezoid.

\boxed{68}

<image>Question: Find x.

\boxed{8\sqrt{2}}

<image>Question: In the figure, m \angle 2 = 110 and m \angle 12 = 55. Find the measure of \angle 2.

\boxed{70}

<image>Question: Find m \angle 1.

\boxed{55}

<image>Question: Find x.

\boxed{2\sqrt{10}}

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

\boxed{164.3}

<image>Question: Find the perimeter of the \triangle D E F, if \triangle D E F \sim \triangle C B F, perimeter of \triangle C B F = 27, D F = 6, F C = 8.

\boxed{20.25}

<image>Question: In quadrilateral A B C D, A C = 188, B D = 214, m \angle B P C = 70, and P is the midpoint of A C and B D. Find the perimeter of quadrilateral A B C D.

\boxed{561.2}

<image>Question: a = 8, b = 15, and c = 17, find \cos B.

\boxed{0.47}

<image>Question: Use parallelogram A B C D to find m \angle B D C.

\boxed{87.9}

<image>Question: What is the value of \tan x?

\boxed{\frac{5}{12}}

<image>Question: Find y.

\boxed{6\sqrt{42}}

<image>Question: Find y.

\boxed{32.6}

<image>Question: Find x. A = 153 in^2.

\boxed{17}

<image>Question: Find m \angle A B D.

\boxed{103}

<image>Question: Find x.

\boxed{4\sqrt{3}}

<image>Question: Find x.

\boxed{2\sqrt{21}}

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

\boxed{20}

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

\boxed{16}

<image>Question: In the figure, m \angle 12 = 64. Find the measure of \angle 8.

\boxed{116}

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

\boxed{9\sqrt2\pi}

<image>Question: In the figure, the vertices of quadrilateral A B C D intersect square E F G H and divide its sides into segments with measure that have a ratio of 1:2. Find the area of A B C D.

\boxed{45}