image imagewidth (px) 139 1.6k | problem stringlengths 13 430 | answer stringclasses 383
values |
|---|---|---|
<image>Find x. | 3 | |
<image>If $\overline{B E} \cong \overline{E D}$ and $m \widehat{E D}=120,$ find $m \widehat{B E}$ | 120 | |
<image>Find x. | 2 \sqrt { 221 } | |
<image>Find $x$ so that $m || n$. | 27 | |
<image>GRID IN In the figure, the radius of circle $A$ is twice the radius of circle $B$ and four times the radius of circle $C .$ If the sum of the circumferences of the three circles is $42 \pi,$ find the measure of $\overline{A C}$
Choose the correct answer from the following options:
A. \frac{252}{13}
B. 27
C. 12
... | B | |
<image>Find $m \angle 2$.
Choose the correct answer from the following options:
A. \( m \angle 2 \) is 114 degrees
B. 70
C. 76
D. 34
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find the area of a regular hexagon with a perimeter of 72 feet.
Choose the correct answer from the following options:
A. for each equilateral triangle:
B. 91.95
C. 374.1
D. 216\sqrt{3} \text{ ft}^2 \text{ or } 432 \text{ ft}^2
Think and explain why do you choose it, then provide your final answer as \boxed{A},... | C | |
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary. | 420 | |
<image>Find the area of the shaded region. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. 127.7 \, \text{sq ft}
B. 89.8 \text{ ft}^2
C. 108.5
D. 75.0 \text{ ft}^2
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>The triangle is inscribed into the circle. Find the exact circumference of the circle. | 12 \pi | |
<image>Find x | 4 | |
<image>Find the area of the shaded sector. Round to the nearest tenth.
Choose the correct answer from the following options:
A. 311.5
B. 69.2
C. 65 degrees.
D. 68.5
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find $x$ in the figure.
Choose the correct answer from the following options:
A. we can set up an equation:
B. 30
C. \[ y° + z° + 48° = 180° \]
D. 16
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find $x$. | 35 | |
<image>In the figure, square $WXYZ$ is inscribed in $\odot R$. Find the measure of a central angle. | 90 | |
<image>Find y.
Choose the correct answer from the following options:
A. we can use \( y \) for both \( x \) and \( y \))
B. 45
C. 8\sqrt{2}
D. we can write the equation as:
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>Find $\angle D$ of quadrilateral ABCD
Choose the correct answer from the following options:
A. measure of angle D is 90 degrees
B. 150^\circ
C. we can set up the following equation:
D. 45
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find $x$. | 70 | |
<image>The diagonals of rhombus FGHJ intersect at K.
If $m\angle FJH = 82$, find $m\angle KHJ$. | 49 | |
<image>Find $y$ in the given parallelogram | 15 | |
<image>Find $HK$.
Choose the correct answer from the following options:
A. 10
B. 0
C. length of $HK$ is $25$
D. 25
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>$\triangle RST \cong \triangle XYZ$. Find $y$. | 15 | |
<image>Find x. Round to the nearest tenth. | 24.7 | |
<image>Find DX if $E X=24$ and $D E=7$
Choose the correct answer from the following options:
A. \text{Insufficient information to determine DX.}
B. 7 \]
C. 25
D. DX = EX - DX = 24 - 7
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>Find $TR$. | 4 | |
<image>Find z | 2 \sqrt { 6 } | |
<image>Find the measure of $\angle 4$ if $m∠4= m∠5$. | 32 | |
<image>Find the perimeter of the triangle. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. perimeter of the triangle is 44
B. 44.5
C. 42.9
D. 43.5
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>If $\overline{QR} \| \overline{XY}, XQ=15, QZ=12$, and $YR=20$, what is the length of $\overline{RZ}$. | 16 | |
<image>Find $x$.
Choose the correct answer from the following options:
A. $x = 16$
B. value of $x$ is $8\sqrt{3}$
C. 13.9
D. $x = \frac{16\sqrt{3}}{3}$
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>In $\odot P$, $PS=4$, find the length of $\widehat {QR}$. Round to the nearest hundredth.
Choose the correct answer from the following options:
A. 23.29
B. $\angle OPR = 2 \times 112° = 224°$
C. 4.75
D. correct interpretation should be:
Think and explain why do you choose it, then provide your final answer as ... | C | |
<image>Find $y$ if $\triangle JLM \sim \triangle QST$. | 4 | |
<image>Find $MP$. | 8 | |
<image>Find x.
Choose the correct answer from the following options:
A. value of \( x \) is \( 8\sqrt{5} \)
B. 24 \sqrt { 2 }
C. \[ 12^2 = 4^2 + y^2 \]
D. 4\sqrt{10}
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>For the pair of similar figures, use the given areas to find $x$.
Choose the correct answer from the following options:
A. unknown side length \( x \) is \( 6\sqrt{3} \) cm
B. value of $x$ is $6 \sqrt{3}$ cm
C. length of $x$ is $54 cm$
D. 10.4
Think and explain why do you choose it, then provide your final ans... | D | |
<image>Find the length of $\widehat {ZY}$. Round to the nearest hundredth. | 5.24 | |
<image>Find the value of x.
Choose the correct answer from the following options:
A. 130
B. 120
C. value of \( x \) is \( 220^\circ \)
D. x = 220 degrees
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find $m \angle A B C$ if $m \widehat{A B}=102$
Choose the correct answer from the following options:
A. 27^\circ
B. 78
C. 51
D. 129
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>If $R T=15, Q P=21,$ and $P T=8,$ find $T S$ | 20 | |
<image>$\triangle K L N$ and $\triangle L M N$ are isosceles and $m \angle J K N=130$. Find the measure of $\angle LKN$.
Choose the correct answer from the following options:
A. 81
B. 110^\circ
C. 135^\circ
D. 105^\circ
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, et... | A | |
<image>Find x. Round the side measure to the nearest tenth.
Choose the correct answer from the following options:
A. 13.2
B. side \( x \) is approximately \( 17
C. 43.7
D. 34.8
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find sinA
Choose the correct answer from the following options:
A. \frac{1}{25}
B. \frac{\sqrt{26}}{5}
C. \sqrt { 26 } / 26
D. \[
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>If XM = 4, XN = 6, and NZ = 9, find XY.
Choose the correct answer from the following options:
A. \frac{20}{3}
B. 8
C. 10
D. \sqrt{261}
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear
to be tangent are tangent. | 8 | |
<image>Find $x$.
Choose the correct answer from the following options:
A. equation becomes:
B. according to the Pythagorean theorem:
C. \sqrt{153}
D. \frac { 26 } { 3 }
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\angle 2$.
Choose the correct answer from the following options:
A. 130
B. 110
C. 50
D. 60
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>Find the measure of $∠A$ to the nearest tenth. | 16.7 | |
<image>Find x. | 2 \sqrt { 13 } | |
<image>Find $ m ∠RSU $ so that $ m \parallel n $. | 124 | |
<image>Find tanB | 5 | |
<image>$RP=3.5$ and $JP=9$. Find $PL$. | 7 | |
<image>If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find SY | 4 | |
<image>Find x. | 2 \sqrt { 5 } | |
<image>The sum of the circumference of circles $H,J,K$ is $56 \pi$ units. Find $KJ$. | 24 | |
<image>Solve for x in the figure below. | 7 | |
<image>Find the measure of $\angle 2$ if $m \angle D G F=53$ and $m \angle A G C=40$. | 50 | |
<image>Find $x$. | 4 | |
<image>Find $m \angle D G E$ | 30 | |
<image>Refer to the figure at the right. Find the value of $x$ if $ p \parallel q $. | 45 | |
<image>Find the length of $WY$ | 9 | |
<image>Find $m\angle U$ | 134 | |
<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 $\angle GFH$.
Choose the correct answer from the following options:
A. \[
B. 92^\circ
C. 68
D. 28^\circ
Think and explain why do you choose it, then provide your fi... | C | |
<image>Find y. | 1.5 | |
<image>If $\overline{PR} \| \overline{KL}, KN=9, LN=16,$ and $PM=2KP$, find $MN$. | 12 | |
<image>Find $NP$.
Choose the correct answer from the following options:
A. NP^2 \]
B. \frac{34}{3}
C. 20
D. 14
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>In the figure, $ \overline{JM} \cong \overline{PM}$ and $ \overline{ML} \cong \overline{PL}$. If $m \angle PLJ=34$, find $m \angle JPM$.
Choose the correct answer from the following options:
A. equal
B. 73^\circ
C. angles $\angle PMJ$ and $\angle PJM$ are equal
D. 36.5
Think and explain why do you choose it, t... | D | |
<image>Find $x$. | 12 | |
<image>Find $x$. | 135 | |
<image>If $\overline{RQ} \cong \overline{RS}$ and $ m ∠RQS = 75 $, find $ m ∠R $. | 30 | |
<image>Find $y$ in the figure. | 40 | |
<image>Find x to the nearest tenth.
Choose the correct answer from the following options:
A. we set up the equation:
B. 150
C. we can set up the equation to solve for \( x \):
D. measure of angle \( x \) is \( 30 \) degrees
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}... | B | |
<image>Find $h$ in each triangle. | 6 \sqrt 3 | |
<image>Find x. | 10 | |
<image>Find $x$. | 18 | |
<image>Find x.
Choose the correct answer from the following options:
A. \( x \)
B. \frac{9}{4}
C. \frac { 4 } { 9 } \sqrt { 3 }
D. value of \( x \) is \( 4\sqrt{3}/9 \)
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>Trapezoid MNPQ has an area of 360 square feet. Find the length of $\overline{MN}$. | 14 | |
<image>Find x. Round side measures to the nearest tenth.
Choose the correct answer from the following options:
A. 15.1
B. equation becomes:
C. all three angles, and we can find angle B:
D. 19.0
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Each pair of polygons is similar. Find CD
Choose the correct answer from the following options:
A. 8
B. 5
C. \frac { 10 } { 3 }
D. \sqrt{13}
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>Find the area of the shaded sector. Round to the nearest tenth. | 7.4 | |
<image>If $\frac{I J}{X J}=\frac{HJ}{YJ}, m \angle W X J=130$, and $m \angle WZG=20,$ find $m \angle JIH$ | 50 | |
<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 $q$. | 7 | |
<image>Find x | 5 \sqrt { 3 } | |
<image>$a=14, b=48,$ and $c=50$ find $cosB$ | 0.28 | |
<image>Find $x$. | 9 | |
<image>$\triangle ABC$ is an isosceles triangle with base $BC$. What is the perimeter of the triangle? | 40 | |
<image>$\overline{XY}$ and $\overline{XZ}$ are midsegments of $\triangle RST$. Find $m \angle RYX$. | 124 | |
<image>Find x. Assume that segments that appear to be tangent are tangent. | 4 | |
<image>Find the perimeter of trapezoid PQRS..
Choose the correct answer from the following options:
A. 10\sqrt{2} + 10\sqrt{3} + 20
B. 38 + 6 \sqrt { 2 } + 6 \sqrt { 3 }
C. PQ + 6\sqrt{3} + 6 + 12 + 10\sqrt{2}
D. QR = 10 * tan(30°) = 10 * (1/√3) = 10√3/3
Think and explain why do you choose it, then provide your final... | B | |
<image>Find $m\angle 3$. | 99 | |
<image>Find $m\angle S$
Choose the correct answer from the following options:
A. 123
B. we have:
C. \frac{175}{3}
D. 58^\circ
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find x. | 4 \sqrt { 3 } | |
<image>Find $y$ so that the quadrilateral is a parallelogram. | 9 | |
<image>Find $x$. | 107 | |
<image>$m∠11 = 4x$, $m∠12 = 2x -6 $. Find the measure of $\angle 12$. | 56 | |
<image>Find $m \angle TUV$ | 53 | |
<image>Find x | 6 | |
<image>Find x | 4 \sqrt { 6 } | |
<image>If $m\angle BAD = 38$ and $m\angle BCD = 50$, find $m\angle ADC$.
Choose the correct answer from the following options:
A. 146
B. 272^\circ
C. 142^\circ
D. based on the information given
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find $m \angle 5$.
Choose the correct answer from the following options:
A. 10°
B. 90°
C. 30°
D. 110
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find the perimeter or circumference of the figure. Round to the nearest tenth. | 25.1 |
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