problem stringlengths 7 242 | answer stringlengths 1 34 | textual_description stringlengths 0 14.2k | images images listlengths 1 1 |
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J is the incenter of \angle A B C. Find J F. | 9 | Equals(MeasureOf(Angle(G, C, B)), 32);Equals(MeasureOf(Angle(G, B, A)), 34);Equals(LengthOf(Line(A, G)), 15);Equals(LengthOf(Line(A, E)), 12);PointLiesOnLine(E, Line(B, A));PointLiesOnLine(D, Line(B, C));PointLiesOnLine(F, Line(A, C));PointLiesOnLine(G, Line(A, D));Perpendicular(Line(C, D), Line(G, D));Perpendicular(Li... | |
In the figure, Q R \parallel T S, Q T \parallel R S, and m \angle 1 = 131. Find the measure of \angle 7. | 49 | Equals(MeasureOf(Angle(J, Q, R)), MeasureOf(angle 1));Equals(MeasureOf(Angle(R, Q, C)), MeasureOf(angle 2));Equals(MeasureOf(Angle(H, R, Q)), MeasureOf(angle 5));Equals(MeasureOf(Angle(Q, T, S)), MeasureOf(angle 3));Equals(MeasureOf(Angle(Q, R, S)), MeasureOf(angle 6));Equals(MeasureOf(Angle(C, T, S)), MeasureOf(angle ... | |
Find y in the parallelogram. | 6 | Equals(MeasureOf(Angle(E, O, C)), 2x+41);Equals(MeasureOf(Angle(E, D, C)), 115);Equals(LengthOf(Line(D, C)), 3y+13);Equals(LengthOf(Line(E, O)), 2y+19) | |
Find the measure of \angle 3. | 14 | Equals(MeasureOf(Angle(E, A, C)), 95);Equals(MeasureOf(Angle(B, D, E)), 109);Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 1));Equals(MeasureOf(Angle(A, B, D)), MeasureOf(angle 3));Equals(MeasureOf(Angle(A, C, D)), MeasureOf(angle 2));Equals(MeasureOf(Angle(E, C, B)), 33);Equals(MeasureOf(Angle(C, B, E)), 24);Point... | |
The degree measure of minor arc \widehat A C and major arc \widehat A D C are x and y respectively. If m \angle A B C = 70, find y. | 250 | Equals(MeasureOf(Minor(Arc(A,C))),x);Equals(MeasureOf(Major(Arc(A,D,C))),y);PointLiesOnCircle(A, Circle(E, radius_3_0));PointLiesOnCircle(C, Circle(E, radius_3_0));PointLiesOnCircle(D, Circle(E, radius_3_0)) | |
Find x. | 32.2 | Equals(LengthOf(Line(A, B)), x);Equals(MeasureOf(Angle(B, A, C)), 25);Equals(LengthOf(Line(B, C)), 15);Perpendicular(Line(A, B), Line(B, C)) | |
What is the value of x if m \widehat N R = 62 and m \widehat N P = 108? | 64 | Equals(MeasureOf(Angle(N, C, P)), 108);Equals(MeasureOf(Angle(N, C, R)), 62);Equals(MeasureOf(Angle(N, M, R)), x);PointLiesOnLine(N, Line(P, M));PointLiesOnCircle(N, Circle(C, radius_6_0));PointLiesOnCircle(P, Circle(C, radius_6_0));PointLiesOnCircle(R, Circle(C, radius_6_0)) | |
Use parallelogram J K L M to find m \angle J M L. | 80 | Equals(LengthOf(Line(J, K)), 2b+3);Equals(LengthOf(Line(J, M)), 3);Equals(LengthOf(Line(L, K)), 21);Equals(MeasureOf(Angle(R, L, K)), 70);Equals(MeasureOf(Angle(M, L, J)), 30);Equals(LengthOf(Line(L, M)), 45);PointLiesOnLine(R, Line(L, J));PointLiesOnLine(R, Line(K, M)) | |
In the figure, m \angle 1 = 3 a + 40, m \angle 2 = 2 a + 25, and m \angle 3 = 5 b - 26. Find b. | 27 | Equals(MeasureOf(Angle(L, W, N)), MeasureOf(angle 1));Equals(MeasureOf(Angle(G, X, E)), MeasureOf(angle 2));Equals(MeasureOf(Angle(I, Y, L)), MeasureOf(angle 7));Equals(MeasureOf(Angle(L, Y, Z)), MeasureOf(angle 6));Equals(MeasureOf(Angle(K, Y, M)), MeasureOf(angle 5));Equals(MeasureOf(Angle(E, Z, K)), MeasureOf(angle ... | |
Polygon B C D E \cong polygon R S T U. Find x. | 20 | Equals(LengthOf(Line(C, B)), 4w-7);Equals(LengthOf(Line(U, T)), z+16);Equals(MeasureOf(Angle(E, B, C)), 2x+9);Equals(MeasureOf(Angle(U, T, S)), y+11);Equals(LengthOf(Line(R, U)), 12);Equals(LengthOf(Line(C, D)), 11);Equals(MeasureOf(Angle(E, D, C)), 2y-31);Equals(MeasureOf(Angle(S, R, U)), 49);Equals(LengthOf(Line(R, S... | |
Find m \angle 3. | 32 | Equals(MeasureOf(Angle(E, D, C)), MeasureOf(Angle(3)));Equals(MeasureOf(Angle(A, B, C)), 32);PointLiesOnLine(E, Line(A, D));PointLiesOnLine(E, Line(B, C));PointLiesOnLine(H, Line(B, C));PointLiesOnLine(E, Line(B, H));PointLiesOnLine(H, Line(E, C));PointLiesOnCircle(A, Circle(H, radius_7_0));PointLiesOnCircle(B, Circle(... | |
Find the area of the figure. Round to the nearest tenth if necessary. | 55.6 | PointLiesOnLine(C, Line(N, E));PointLiesOnLine(I, Line(N, E));PointLiesOnLine(C, Line(N, I));PointLiesOnLine(C, Line(N, J));PointLiesOnLine(D, Line(B, P));PointLiesOnLine(B, Line(D, O));PointLiesOnLine(B, Line(O, L));PointLiesOnLine(B, Line(O, P));PointLiesOnLine(D, Line(O, P));PointLiesOnLine(I, Line(C, E));PointLiesO... | |
Find x. | 22 | Equals(MeasureOf(Arc(D, F)), 24);Equals(MeasureOf(Angle(F, B, D)), x);Equals(MeasureOf(Arc(A, C)), 68);PointLiesOnLine(D, Line(A, B));PointLiesOnLine(F, Line(B, C));PointLiesOnCircle(A, Circle(E, radius_4_0));PointLiesOnCircle(C, Circle(E, radius_4_0));PointLiesOnCircle(D, Circle(E, radius_4_0));PointLiesOnCircle(F, Ci... | |
Find A C if A C = x - 3, B E = 20, A B = 16, and C D = x + 5. | 32 | PointLiesOnLine(B, Line(E, A));PointLiesOnLine(C, Line(A, D));Parallel(Line(C, B), Line(E, D)) | |
J H, J P, and P H are midsegments of \triangle K L M. Find x. | 60 | Equals(MeasureOf(Angle(L, J, H)), x);Equals(MeasureOf(Angle(M, H, P)), 44);Equals(MeasureOf(Angle(J, H, L)), 76);PointLiesOnLine(J, Line(K, L));PointLiesOnLine(P, Line(K, M));PointLiesOnLine(H, Line(M, L)) | |
Find the value of the variable w. | 8 | Equals(LengthOf(Line(B, C)), 36);Equals(LengthOf(Line(B, D)), w+4);Equals(LengthOf(Line(A, D)), 6);Equals(LengthOf(Line(C, D)), 24);PointLiesOnLine(D, Line(A, C));Perpendicular(Line(B, C), Line(A, B));Perpendicular(Line(B, D), Line(C, D)) | |
Find x. | 11 | Equals(MeasureOf(Angle(Y, W, X)), 52);Equals(MeasureOf(Angle(W, X, Y)), 6y-2);Equals(MeasureOf(Angle(W, Y, X)), 4x+20);Equals(LengthOf(Line(W, X)), LengthOf(Line(W, Y))) | |
Find x. Assume that segments that appear to be tangent are tangent. | 7 | Equals(LengthOf(Line(C, E)), 7);Equals(LengthOf(Line(E, D)), x);PointLiesOnCircle(B, Circle(C, radius_2_0));PointLiesOnCircle(E, Circle(C, radius_2_0));Perpendicular(Line(C, E), Line(E, D));Perpendicular(Line(C, B), Line(B, D)) | |
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent. | 6 | Equals(LengthOf(Line(A, F)), x);Equals(LengthOf(Line(D, E)), 9);Equals(LengthOf(Line(A, E)), 3);PointLiesOnLine(E, Line(A, B));PointLiesOnLine(B, Line(A, D));PointLiesOnLine(E, Line(A, D));PointLiesOnLine(B, Line(D, E));PointLiesOnCircle(D, Circle(B, radius_1_0));PointLiesOnCircle(E, Circle(B, radius_1_0));PointLiesOnC... | |
If J, P, and L are the midpoints of K H, H M and M K, respectively. Find z. | 1 | Equals(LengthOf(Line(Q, H)), y);Equals(LengthOf(Line(Q, J)), 2z);Equals(LengthOf(Line(Q, P)), 2x-6);Equals(LengthOf(Line(Q, K)), 7);Equals(LengthOf(Line(Q, L)), 3);Equals(LengthOf(Line(Q, M)), 4);PointLiesOnLine(J, Line(K, H));PointLiesOnLine(L, Line(K, M));PointLiesOnLine(Q, Line(K, P));PointLiesOnLine(P, Line(H, M));... | |
The segment is tangent to the circle. Find x. | 4 | Equals(LengthOf(Line(E, B)), 3x);Equals(LengthOf(Line(B, C)), 5x-8);PointLiesOnCircle(C, Circle(R, radius_3_0));PointLiesOnCircle(E, Circle(R, radius_3_0)) | |
Find \sin A. | \sqrt { 26 } / 26 | Equals(LengthOf(Line(A, C)), 5\sqrt{26});Equals(MeasureOf(Angle(D, C, A)), x);Equals(LengthOf(Line(C, D)), 5);Equals(LengthOf(Line(C, B)), \sqrt{26});Equals(LengthOf(Line(A, D)), 25);Equals(LengthOf(Line(D, B)), 1);PointLiesOnLine(D, Line(A, B));Perpendicular(Line(A, C), Line(C, B));Perpendicular(Line(C, D), Line(A, B)... | |
In the figure, \triangle F G H is a right triangle with hypotenuse F H and G J = G H. What is the measure of \angle J G H? | 56 | Equals(MeasureOf(Angle(H, F, G)), 28);PointLiesOnLine(J, Line(F, H)) | |
In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 5. | 60 | Equals(MeasureOf(Angle(M, J, B)), MeasureOf(angle 1));Equals(MeasureOf(Angle(E, P, C)), MeasureOf(angle 2));Equals(MeasureOf(Angle(A, G, K)), MeasureOf(angle 3));Equals(MeasureOf(Angle(P, O, R)), MeasureOf(angle 4));Equals(MeasureOf(Angle(P, R, O)), MeasureOf(angle 5));Equals(MeasureOf(Angle(O, P, R)), MeasureOf(angle ... | |
Find m \angle 3. | 68 | Equals(MeasureOf(Angle(E, A, D)), MeasureOf(angle 3));Equals(MeasureOf(Angle(A, F, C)), MeasureOf(angle 2));Equals(MeasureOf(Angle(F, B, D)), 50);Equals(MeasureOf(Angle(G, F, D)), MeasureOf(angle 1));Equals(MeasureOf(Angle(E, G, F)), 120);Equals(MeasureOf(Angle(H, G, E)), MeasureOf(angle 4));Equals(MeasureOf(Angle(H, C... | |
Find \angle D of quadrilateral A B C D. | 45 | Equals(MeasureOf(Angle(B, A, D)), 3x);Equals(MeasureOf(Angle(A, D, C)), x);Perpendicular(Line(B, A), Line(C, B));Perpendicular(Line(C, B), Line(C, D)) | |
Find z. | 10 \sqrt { 2 } | Equals(LengthOf(Line(A, B)), z);Equals(LengthOf(Line(B, Y)), 15);Equals(LengthOf(Line(A, C)), 5);PointLiesOnLine(Y, Line(B, C));Perpendicular(Line(B, Y), Line(A, Y));Perpendicular(Line(A, B), Line(A, C)) | |
Find x. | 60 | Equals(MeasureOf(Angle(Y, V, W)), 25);Equals(MeasureOf(Angle(Z, A, X)), 110);Equals(MeasureOf(Angle(Y, A, W)), x);PointLiesOnLine(Y, Line(V, B));PointLiesOnLine(Z, Line(V, B));PointLiesOnLine(X, Line(V, C));PointLiesOnLine(W, Line(V, C));PointLiesOnLine(Y, Line(V, Z));PointLiesOnLine(W, Line(V, X));PointLiesOnLine(Z, L... | |
Find x. | 8 | Equals(LengthOf(Line(A, B)), 13);Equals(LengthOf(Line(A, L)), 5);Equals(LengthOf(Line(B, N)), x);Equals(LengthOf(Line(C, N)), 7);Equals(LengthOf(Line(D, L)), 6);PointLiesOnLine(M, Line(A, B));PointLiesOnLine(L, Line(A, D));PointLiesOnLine(N, Line(B, C));PointLiesOnLine(P, Line(D, C));PointLiesOnCircle(P, Circle(Q, radi... | |
If W P is a perpendicular bisector, m \angle W H A = 8 q + 17, m \angle H W P = 10 + q, A P = 6 r + 4, and P H = 22 + 3 r, find r. | 6 | PointLiesOnLine(Q, Line(W, A));PointLiesOnLine(X, Line(W, P));PointLiesOnLine(P, Line(H, A));PointLiesOnLine(X, Line(H, Q)); | |
Find K L. | 6 | Equals(LengthOf(Line(L, J)), 12);Perpendicular(Line(J, K), Line(K, M));Equals(LengthOf(Line(J, M)), LengthOf(Line(L, M)));PointLiesOnLine(K, Line(J, L)) | |
If Q R \parallel X Y, X Q = 15, Q Z = 12, and Y R = 20, what is the length of R Z. | 16 | PointLiesOnLine(R, Line(Z, Y));PointLiesOnLine(Q, Line(Z, X)) | |
Find y. Round to the nearest tenth. | 11.7 | Equals(LengthOf(Line(A, D)), 8);Equals(LengthOf(Line(A, C)), x);Equals(MeasureOf(Angle(B, C, A)), 43);Equals(LengthOf(Line(B, D)), y);PointLiesOnLine(A, Line(C, D));Perpendicular(Line(A, C), Line(A, B));Perpendicular(Line(B, D), Line(B, C)) | |
Find m \angle E. | 158 | Equals(MeasureOf(Angle(A, E, D)), 2x+10);Equals(MeasureOf(Angle(C, D, E)), x);Equals(MeasureOf(Angle(B, C, D)), 2x-20);PointLiesOnLine(F, Line(A, E));Perpendicular(Line(F, A), Line(A, B));Perpendicular(Line(A, B), Line(C, B)) | |
Find y. | 8 | Equals(LengthOf(Line(E, B)), 12-2x);Equals(LengthOf(Line(A, D)), 7y);Equals(LengthOf(Line(C, E)), 8x-18);Equals(LengthOf(Line(C, A)), 5y+16);PointLiesOnLine(E, Line(C, B));PointLiesOnLine(A, Line(C, D));Equals(MeasureOf(Angle(B, D, A)), MeasureOf(Angle(E, A, C))) | |
Find X Y. | 21 | Equals(LengthOf(Line(Y, Z)), 4x+5);Equals(MeasureOf(Angle(B, W, Y)), 33);Equals(MeasureOf(Angle(C, W, A)), 33);Equals(LengthOf(Line(X, Y)), 6x-3);PointLiesOnLine(X, Line(W, A));PointLiesOnLine(Z, Line(W, B));PointLiesOnLine(Y, Line(W, C));Perpendicular(Line(W, Z), Line(Y, Z));Perpendicular(Line(Y, X), Line(W, X)) | |
Find \angle W. | 134 | Equals(MeasureOf(Angle(V, U, T)), 3x-4);Equals(MeasureOf(Angle(W, V, U)), x);Equals(MeasureOf(Angle(T, W, V)), 3x-4);Equals(MeasureOf(Angle(U, T, W)), x) | |
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 22.7 | Equals(LengthOf(Line(D, F)), 4.2);Equals(LengthOf(Line(B, D)), 5.4);Perpendicular(Line(E, B), Line(B, D));Equals(LengthOf(Line(E, B)), LengthOf(Line(D, F)));Equals(LengthOf(Line(E, F)), LengthOf(Line(D, B))) | |
m \angle B A C = 40, m \angle D A C = 40, and D C = 10, find B C. | 10 | PointLiesOnLine(C, Line(E, A));PointLiesOnLine(B, Line(E, F));PointLiesOnLine(D, Line(E, N));Perpendicular(Line(B, F), Line(C, B));Perpendicular(Line(C, D), Line(D, N)) | |
Find x. | 20 | Equals(LengthOf(Line(A, B)), 25);Equals(LengthOf(Line(B, C)), 15);Equals(LengthOf(Line(A, C)), x);Perpendicular(Line(B, C), Line(A, C)) | |
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 471.9 | Equals(LengthOf(Line(D, N)), 18);Equals(LengthOf(Line(B, N)), 22);Equals(MeasureOf(Angle(N, A, D)), 40);PointLiesOnLine(N, Line(B, D));Perpendicular(Line(A, D), Line(D, N)) | |
Find the perimeter of the triangle. Round to the nearest tenth if necessary. | 36 | Equals(LengthOf(Line(A, B)), 15);Equals(LengthOf(Line(A, C)), 9);Equals(LengthOf(Line(B, C)), 12);Perpendicular(Line(A, C), Line(B, C)) | |
Find the perimeter or circumference of the figure. Round to the nearest tenth. | 8.6 | Equals(LengthOf(Line(A, B)), 3.2);Equals(LengthOf(Line(A, C)), 1.1) | |
Find m \angle 4. | 64 | Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 1));Equals(MeasureOf(Angle(F, B, A)), MeasureOf(angle 2));Equals(MeasureOf(Angle(F, A, C)), MeasureOf(angle 4));Equals(MeasureOf(Angle(D, B, F)), MeasureOf(angle 3));Equals(MeasureOf(Angle(A, D, B)), 64);PointLiesOnLine(F, Line(D, A));PointLiesOnLine(E, Line(D, C));Poin... | |
Find the area of the figure. Round to the nearest tenth. | 91.2 | Equals(LengthOf(Line(A, C)), 6);Equals(LengthOf(Line(A, F)), 5);Equals(LengthOf(Line(F, D)), 6);Equals(LengthOf(Line(F, D)), 12);PointLiesOnLine(H, Line(F, D));Perpendicular(Line(G, H), Line(F, H));Equals(LengthOf(Line(B, E)), LengthOf(Line(G, E)));Equals(LengthOf(Line(G, E)), LengthOf(Line(G, C)));Equals(LengthOf(Line... | |
Find the measure of R T of equilateral triangle R S T if R S = x + 9, S T = 2 x, and R T = 3 x - 9. | 18 | Equals(LengthOf(Line(T, A)), 2x);Equals(LengthOf(Line(R, A)), x+9);Equals(LengthOf(Line(R, T)), 3x-9) | |
Find U B if \triangle R S T \sim \triangle U V W, T A and W B are medians, T A = 8, R A = 3, W B = 3 x - 6, and U B = x + 2. | 36 | PointLiesOnLine(B, Line(U, V));PointLiesOnLine(A, Line(R, S)) | |
Solve for x in the figure below. | 31 | Equals(MeasureOf(Angle(K, H, G)), 65);Equals(MeasureOf(Angle(L, D, F)), 4x-9);PointLiesOnLine(D, Line(B, L));PointLiesOnLine(H, Line(D, G));PointLiesOnLine(H, Line(E, K));PointLiesOnLine(D, Line(H, F));PointLiesOnLine(D, Line(F, G));PointLiesOnLine(H, Line(F, G));Parallel(Line(B,L), Line(E,K)) | |
Q S is a diameter of \odot V. Find m \widehat S T P. | 147 | Equals(MeasureOf(Angle(T, V, S)), 75);Equals(MeasureOf(Angle(P, V, T)), 72);PointLiesOnLine(V, Line(S, Q));PointLiesOnCircle(S, Circle(V, radius_1_0));PointLiesOnCircle(P, Circle(V, radius_1_0));PointLiesOnCircle(R, Circle(V, radius_1_0));PointLiesOnCircle(T, Circle(V, radius_1_0));PointLiesOnCircle(Q, Circle(V, radius... | |
Find m \angle K. | 117 | Equals(MeasureOf(Angle(K, J, M)), 59);Equals(MeasureOf(Angle(M, L, K)), 67);Equals(LengthOf(Line(J, M)), LengthOf(Line(J, K)));Equals(LengthOf(Line(M, L)), LengthOf(Line(L, K))) | |
In the figure, J M \cong P M and M L \cong P L. If m \angle P L J = 58, find m \angle P J L. | 30.5 | PointLiesOnLine(M, Line(L, J)) | |
In quadrilateral P Q R S, P Q = 721, Q R = 547, R S = 593, P S = 756, and m \angle P = 58. Find Q S. | 716.7 | ||
In \odot P, R T = 11, find m \widehat Q R S. Round to the nearest hundredth. | 19.01 | Equals(MeasureOf(Angle(R, P, S)), 130);Equals(MeasureOf(Angle(T, P, Q)), 112);PointLiesOnLine(P, Line(T, R));PointLiesOnCircle(S, Circle(P, radius_5_0));PointLiesOnCircle(T, Circle(P, radius_5_0));PointLiesOnCircle(R, Circle(P, radius_5_0));PointLiesOnCircle(Q, Circle(P, radius_5_0)) | |
According to the Perpendicular Bisector Theorem, what is the length of segment A B below? | 2.5 | Equals(LengthOf(Line(D, A)), 2.5);PointLiesOnLine(C, Line(D, B));PointLiesOnLine(A, Line(C, F));PointLiesOnLine(C, Line(A, G));PointLiesOnLine(A, Line(F, G));PointLiesOnLine(C, Line(F, G));Perpendicular(Line(A, C), Line(C, B));Equals(LengthOf(Line(D, C)), LengthOf(Line(C, B))) | |
Use parallelogram A B C D to find B C. | 9 | Equals(MeasureOf(Angle(F, A, D)), 20);Equals(LengthOf(Line(D, A)), 9);Equals(MeasureOf(Angle(F, A, B)), 32);Equals(LengthOf(Line(B, A)), 6);Equals(LengthOf(Line(D, C)), 6.86);Equals(MeasureOf(Angle(F, B, C)), 40.1);PointLiesOnLine(F, Line(D, B));PointLiesOnLine(F, Line(C, A)) | |
Find x. | 5 \sqrt { 3 } | Equals(MeasureOf(Angle(B, A, C)), 60);Equals(LengthOf(Line(A, B)), y);Equals(LengthOf(Line(A, C)), 5);Equals(LengthOf(Line(B, C)), x);Perpendicular(Line(A, C), Line(B, C)) | |
Circle A has diameters D F and P G. If A G = 12, find L A. | 12 | PointLiesOnLine(A, Line(F, D));PointLiesOnLine(A, Line(P, G));PointLiesOnCircle(L, Circle(A, radius_0_0));PointLiesOnCircle(F, Circle(A, radius_0_0));PointLiesOnCircle(P, Circle(A, radius_0_0));PointLiesOnCircle(G, Circle(A, radius_0_0));PointLiesOnCircle(D, Circle(A, radius_0_0)) | |
Find the area of the figure. | 938.4 | Equals(LengthOf(Line(H, B)), 30);Equals(LengthOf(Line(A, H)), 15);Equals(LengthOf(Line(A, D)), 48);PointLiesOnLine(H, Line(A, C));PointLiesOnLine(J, Line(A, C));PointLiesOnLine(F, Line(A, D));PointLiesOnLine(I, Line(A, D));PointLiesOnLine(I, Line(A, F));PointLiesOnLine(J, Line(A, H));PointLiesOnLine(H, Line(C, J));Poin... | |
Find m \angle 4. | 15 | Equals(MeasureOf(Angle(F, A, D)), MeasureOf(angle 1));Equals(MeasureOf(Angle(A, F, C)), 70);Equals(MeasureOf(Angle(C, E, B)), MeasureOf(angle 2));Equals(MeasureOf(Angle(A, B, C)), MeasureOf(angle 3));Equals(MeasureOf(Angle(B, C, E)), MeasureOf(angle 4));Equals(MeasureOf(Angle(F, B, E)), 35);PointLiesOnLine(F, Line(A, B... | |
If \frac { I J } { X J } = \frac { H J } { Y J }, m \angle W X J = 130, and m \angle W Z G = 20, find m \angle J I H. | 50 | Equals(MeasureOf(Angle(Y, Z, I)), 20);Equals(MeasureOf(Angle(W, X, J)), 130);PointLiesOnLine(H, Line(G, I));PointLiesOnLine(H, Line(G, Z));PointLiesOnLine(I, Line(H, Z));PointLiesOnLine(I, Line(G, Z));PointLiesOnLine(H, Line(J, X));PointLiesOnLine(I, Line(J, Y));PointLiesOnLine(X, Line(W, Y));PointLiesOnLine(X, Line(W,... | |
In \odot A, m \angle E A D = 42. Find m \widehat C B E. | 180 | Equals(MeasureOf(Angle(E, A, D)), 42);PointLiesOnLine(A, Line(D, B));PointLiesOnLine(A, Line(E, C));PointLiesOnCircle(D, Circle(A, radius_2_0));PointLiesOnCircle(B, Circle(A, radius_2_0));PointLiesOnCircle(E, Circle(A, radius_2_0));PointLiesOnCircle(C, Circle(A, radius_2_0)) | |
Find the area of the circle. Round to the nearest tenth. | 113.1 | Equals(LengthOf(Line(A, B)), 6);PointLiesOnCircle(A, Circle(B, radius_1_0)) | |
Find x. | 6 | Equals(LengthOf(Line(A, B)), 15);Equals(LengthOf(Line(B, C)), 10);Equals(LengthOf(Line(C, D)), 4);Equals(LengthOf(Line(A, D)), x);PointLiesOnLine(D, Line(A, C));Equals(MeasureOf(Angle(C, B, D)), MeasureOf(Angle(D, B, A))) | |
Find x. | 70 | PointLiesOnCircle(A, Circle(E, radius_4_0));PointLiesOnCircle(B, Circle(E, radius_4_0));PointLiesOnCircle(C, Circle(E, radius_4_0));PointLiesOnCircle(D, Circle(E, radius_4_0));Equals(MeasureOf(Angle(D,E,C)), 110);Equals(MeasureOf(Angle(A,E,B)), 110);Equals(MeasureOf(Angle(D,E,A)), x);Equals(MeasureOf(Angle(C,E,B)), x) | |
Find the area of the triangle. Round to the nearest tenth if necessary. | 129.9 | Equals(LengthOf(Line(A, N)), 10);Equals(LengthOf(Line(B, C)), 30);Equals(LengthOf(Line(C, N)), 5);PointLiesOnLine(C, Line(B, N));Perpendicular(Line(A, C), Line(C, N)) | |
Find E G. | 10 | Equals(LengthOf(Line(G, F)), 5);Equals(LengthOf(Line(G, D)), 6.5);Equals(LengthOf(Line(E, D)), 6.5);PointLiesOnLine(F, Line(E, G));PointLiesOnLine(F, Line(D, Y));PointLiesOnLine(D, Line(F, A));PointLiesOnLine(D, Line(A, Y));PointLiesOnLine(F, Line(A, Y));Perpendicular(Line(D, F), Line(E, F)) | |
Find x. Assume that segments that appear to be tangent are tangent. | 9.6 | Equals(LengthOf(Line(D, E)), 5);Equals(LengthOf(Line(A, D)), 8);Equals(LengthOf(Line(D, F)), 6);PointLiesOnLine(D, Line(A, F));PointLiesOnLine(D, Line(B, E));PointLiesOnCircle(A, Circle(C, radius_5_0));PointLiesOnCircle(B, Circle(C, radius_5_0));PointLiesOnCircle(E, Circle(C, radius_5_0));PointLiesOnCircle(F, Circle(C,... | |
If m \angle 2 = 4 x + 7 and m \angle 7 = 5 x - 13, find x. | 20 | Equals(MeasureOf(Angle(K, M, P)), MeasureOf(angle 7));Equals(MeasureOf(Angle(K, M, H)), MeasureOf(angle 5));Equals(MeasureOf(Angle(D, M, P)), MeasureOf(angle 8));Equals(MeasureOf(Angle(G, H, M)), MeasureOf(angle 3));Equals(MeasureOf(Angle(D, M, H)), MeasureOf(angle 6));Equals(MeasureOf(Angle(G, H, E)), MeasureOf(angle ... | |
Use parallelogram N Q R M to find x. | 4 | Equals(LengthOf(Line(N, Q)), 3x+2);Equals(LengthOf(Line(Q, L)), 12);Equals(LengthOf(Line(N, M)), 2y+5);Equals(LengthOf(Line(R, Q)), 3y);Equals(LengthOf(Line(M, L)), LengthOf(w));Equals(LengthOf(Line(R, M)), 4x-2);PointLiesOnLine(L, Line(N, R));PointLiesOnLine(L, Line(Q, M)) | |
Suppose B D = 12 millimeters. Find the radius of the circle. | 6 | PointLiesOnLine(E, Line(B, D));PointLiesOnLine(E, Line(A, C));PointLiesOnCircle(B, Circle(E, radius_1_0));PointLiesOnCircle(A, Circle(E, radius_1_0));PointLiesOnCircle(D, Circle(E, radius_1_0));PointLiesOnCircle(C, Circle(E, radius_1_0)) | |
For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure. | \frac { 5 } { 3 } | Equals(LengthOf(HeightOf(Triangle(A,B,C))), x);Equals(LengthOf(HeightOf(Triangle(D,E,F))), 21);Equals(AreaOf(Triangle(A, B, C)), 875);Equals(AreaOf(Triangle(D, E, F)), 315) | |
Find x. Round to the nearest tenth. | 7.1 | Equals(MeasureOf(Angle(C, A, B)), 78);Equals(LengthOf(Line(C, A)), x);Equals(MeasureOf(Angle(A, B, C)), 60);Equals(LengthOf(Line(C, B)), 8) | |
Find the value of x. | 4.08 | Equals(MeasureOf(Angle(X, A, N)), 78);Equals(LengthOf(Line(X, A)), 3);Equals(LengthOf(Arc(X, N)), x);PointLiesOnCircle(X, Circle(A, radius_1_0));PointLiesOnCircle(N, Circle(A, radius_1_0)) | |
The pair of polygons is similar. Find A B. | 4 | Equals(LengthOf(Line(E, B)), 5);Equals(LengthOf(Line(A, B)), x-2);Equals(LengthOf(Line(A, D)), x);Equals(LengthOf(Line(D, G)), 75);PointLiesOnLine(B, Line(E, A));PointLiesOnLine(D, Line(A, G)) | |
The diameters of \odot A, \odot B, and \odot C are 8 inches, 18 inches, and 11 inches, respectively. Find F G. | 14 | PointLiesOnLine(F, Line(A, C));PointLiesOnLine(B, Line(A, C));PointLiesOnLine(F, Line(A, G));PointLiesOnLine(C, Line(A, G));PointLiesOnLine(B, Line(A, G));PointLiesOnLine(F, Line(A, B));PointLiesOnLine(B, Line(F, C));PointLiesOnLine(B, Line(F, G));PointLiesOnCircle(A, Circle(B, radius_0_1));PointLiesOnCircle(G, Circle(... | |
Find the area of the figure. Round to the nearest tenth if necessary. | 99 | Equals(LengthOf(Line(E, S)), 4);Equals(LengthOf(Line(L, B)), 6);Equals(LengthOf(Line(N, B)), 18);Equals(LengthOf(Line(A, N)), 21);Equals(LengthOf(Line(A, N)), LengthOf(n)) | |
Find m \widehat A C. | 48 | Equals(MeasureOf(Angle(A, D, C)), 24);PointLiesOnCircle(B, Circle(D, radius_3_0));PointLiesOnCircle(A, Circle(D, radius_3_0));PointLiesOnCircle(C, Circle(D, radius_3_0)) | |
In rhombus A B C D, A B = 2 x + 3 and B C = 5 x. Find x. | 1 | PointLiesOnLine(E, Line(D, B));PointLiesOnLine(E, Line(C, A)) | |
Find m \angle C. | 127 | Equals(MeasureOf(Angle(A, B, C)), x-8);Equals(MeasureOf(Angle(F, A, B)), x+2);Equals(MeasureOf(Angle(B, C, D)), x+7);Equals(MeasureOf(Angle(A, F, E)), x-4);Equals(MeasureOf(Angle(F, E, D)), x+6);Equals(MeasureOf(Angle(C, E, D)), x-3) | |
Find x. | 24 | Equals(LengthOf(Line(M, X)), 5);Equals(LengthOf(Line(M, J)), 13);PointLiesOnLine(X, Line(R, S));PointLiesOnCircle(J, Circle(M, radius_0_0));PointLiesOnCircle(S, Circle(M, radius_0_0));PointLiesOnCircle(R, Circle(M, radius_0_0));Perpendicular(Line(X, R), Line(M, X)) | |
Find the perimeter of the figure in feet. Round to the nearest tenth, if necessary. | 28 | Equals(LengthOf(Line(A, B)), 12);Equals(LengthOf(Line(C, D)), 8);Equals(MeasureOf(Angle(A, D, E)), 30);PointLiesOnLine(E, Line(A, B));Perpendicular(Line(D, E), Line(E, A));Equals(LengthOf(Line(D, A)), LengthOf(Line(C, B))) | |
Find x. Assume that segments that appear to be tangent are tangent. | 8 | Equals(LengthOf(Line(O, N)), 6);Equals(LengthOf(Line(P, N)), x);Equals(LengthOf(Line(P, O)), 10);PointLiesOnLine(A, Line(P, O));PointLiesOnCircle(N, Circle(O, radius_1_0));PointLiesOnCircle(A, Circle(O, radius_1_0)) | |
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent. | 14 | Equals(LengthOf(Line(B, K)), x+2);Equals(LengthOf(Line(B, J)), x);Equals(LengthOf(Line(L, B)), x+10);Equals(LengthOf(Line(B, M)), x+7);PointLiesOnLine(B, Line(L, J));PointLiesOnLine(B, Line(M, K));PointLiesOnCircle(L, Circle(O, radius_5_0));PointLiesOnCircle(M, Circle(O, radius_5_0));PointLiesOnCircle(K, Circle(O, radi... | |
In the figure, m \angle 12 = 64. Find the measure of \angle 13. | 64 | Equals(MeasureOf(Angle(I, D, W)), MeasureOf(angle 1));Equals(MeasureOf(Angle(W, D, L)), MeasureOf(angle 2));Equals(MeasureOf(Angle(D, U, A)), MeasureOf(angle 3));Equals(MeasureOf(Angle(A, U, L)), MeasureOf(angle 4));Equals(MeasureOf(Angle(H, D, I)), MeasureOf(angle 5));Equals(MeasureOf(Angle(L, D, H)), MeasureOf(angle ... | |
Find y. | 32.6 | Equals(LengthOf(Line(C, A)), x);Equals(LengthOf(Line(C, B)), 24);Equals(MeasureOf(Angle(C, A, B)), 32);PointLiesOnLine(D, Line(A, B));Perpendicular(Line(C, A), Line(C, B));Perpendicular(Line(C, D), Line(A, D)) | |
Find x. | 4 | Equals(LengthOf(Line(A, W)), 4);Equals(MeasureOf(Angle(W, A, R)), l);Equals(LengthOf(Line(R, W)), 4);Equals(MeasureOf(Angle(W, A, R)), n);Equals(MeasureOf(Angle(W, A, R)), w);Equals(LengthOf(Line(W, L)), 8);Equals(LengthOf(Line(W, L)), 12);PointLiesOnLine(L, Line(R, W)) | |
Quadrilateral A B C D is inscribed in \odot Z such that m \angle B Z A = 104, m \widehat C B = 94, and A B \parallel D C. Find m \widehat B A. | 104 | PointLiesOnLine(E, Line(D, B));PointLiesOnLine(E, Line(A, C));PointLiesOnCircle(D, Circle(Z, radius_4_0));PointLiesOnCircle(B, Circle(Z, radius_4_0));PointLiesOnCircle(A, Circle(Z, radius_4_0));PointLiesOnCircle(C, Circle(Z, radius_4_0)) | |
If x = 7 \sqrt { 3 }, find C E. | 21 | Equals(MeasureOf(Angle(C, B, E)), 60);Equals(LengthOf(Line(E, A)), y);Equals(LengthOf(Line(C, B)), LengthOf(a));Equals(MeasureOf(Angle(C, A, B)), 30);Equals(LengthOf(Line(A, C)), LengthOf(b));PointLiesOnLine(E, Line(A, B));Perpendicular(Line(E, A), Line(E, C));Perpendicular(Line(E, C), Line(A, C)) | |
Find H K. | 10 | Equals(LengthOf(Line(P, N)), 8);Equals(LengthOf(Line(N, Q)), 12);Equals(LengthOf(Line(P, Q)), 20);Equals(LengthOf(Line(J, H)), 4x+7);Equals(LengthOf(Line(J, K)), 25);Equals(LengthOf(Line(K, H)), 6x-2);Equals(MeasureOf(Angle(H, J, K)), MeasureOf(Angle(P, Q, N)));Equals(MeasureOf(Angle(J, H, K)), MeasureOf(Angle(P, N, Q)... | |
Find x. | 2 | Equals(LengthOf(Line(Q, B')), 8);Equals(LengthOf(Line(B, Q)), 6);Equals(LengthOf(Line(B, B')), x);PointLiesOnLine(D, Line(Q, A));PointLiesOnLine(B, Line(Q, B')) | |
Find the measure of \angle 1. | 70 | Equals(MeasureOf(Angle(E, C, B)), 82);Equals(MeasureOf(Angle(C, B, A)), 28);Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 1));Equals(MeasureOf(Angle(A, E, D)), MeasureOf(angle 2));Equals(MeasureOf(Angle(D, A, E)), 68);Equals(MeasureOf(Angle(C, D, A)), MeasureOf(angle 3));PointLiesOnLine(E, Line(A, B));PointLiesOnLi... | |
The segment is tangent to the circle. Find x. | 9 | Equals(LengthOf(Line(B, C)), 12);Equals(LengthOf(Line(E, C)), 6);Equals(LengthOf(Line(A, B)), x);Equals(LengthOf(Line(A, E)), x);;PointLiesOnCircle(E, Circle(A, radius_7_0));PointLiesOnCircle(B, Circle(A, radius_7_0)) | |
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth. | 4.1 | Equals(LengthOf(Line(G, F)), 4.1);PointLiesOnLine(F, Line(A, B));PointLiesOnLine(J, Line(B, D));PointLiesOnLine(A, Line(B, G));PointLiesOnLine(F, Line(B, G));PointLiesOnLine(L, Line(B, H));PointLiesOnLine(A, Line(F, G));PointLiesOnLine(K, Line(G, C));PointLiesOnCircle(E, Circle(F, radius_5_0));PointLiesOnCircle(H, Circ... | |
The segment is tangent to the circle. Find x. | 5 \sqrt { 10 } | Equals(LengthOf(Line(F, B)), 15);Equals(LengthOf(Line(D, F)), 5);Equals(LengthOf(Line(D, B)), x);PointLiesOnCircle(F, Circle(D, radius_3_0)) | |
Quadrilateral W X Z Y is a rhombus. If m \angle X Z Y = 56, find m \angle Y W Z. | 28 | Equals(MeasureOf(Angle(Y, X, W)), MeasureOf(angle 1));Equals(MeasureOf(Angle(Z, X, T)), MeasureOf(angle 2));Equals(MeasureOf(Angle(W, T, X)), MeasureOf(angle 3));PointLiesOnLine(T, Line(Z, W));PointLiesOnLine(T, Line(Y, X)) | |
Find x. Round side measure to the nearest tenth. | 30.0 | Equals(MeasureOf(Angle(C, A, B)), 73);Equals(LengthOf(Line(A, B)), 32);Equals(LengthOf(Line(A, C)), x);Equals(MeasureOf(Angle(A, B, C)), 51) | |
Find x in the figure. | 31 | Equals(MeasureOf(Angle(H, N, K)), 4x);Equals(MeasureOf(Angle(N, M, O)), 56);Equals(MeasureOf(Angle(T, L, G)), 3y-11);PointLiesOnLine(J, Line(A, C));PointLiesOnLine(U, Line(A, C));PointLiesOnLine(U, Line(A, L));PointLiesOnLine(L, Line(A, Q));PointLiesOnLine(U, Line(A, Q));PointLiesOnLine(A, Line(C, T));PointLiesOnLine(J... | |
Find x. | 8 \sqrt { 3 } | Equals(LengthOf(Line(B, C)), y);Equals(LengthOf(Line(B, D)), 12);Equals(MeasureOf(Angle(B, C, A)), 60);PointLiesOnLine(D, Line(A, C));Perpendicular(Line(B, D), Line(A, D));Equals(LengthOf(Line(A, B)), LengthOf(Line(B, C))) | |
Q S is a diameter of \odot V. Find m \widehat Q R T. | 255 | Equals(MeasureOf(Angle(T, V, S)), 75);Equals(MeasureOf(Angle(P, V, T)), 72);PointLiesOnLine(V, Line(S, Q));PointLiesOnCircle(S, Circle(V, radius_1_0));PointLiesOnCircle(P, Circle(V, radius_1_0));PointLiesOnCircle(R, Circle(V, radius_1_0));PointLiesOnCircle(T, Circle(V, radius_1_0));PointLiesOnCircle(Q, Circle(V, radius... | |
Find x. | 6 | Equals(LengthOf(Line(A, D)), 4);Equals(LengthOf(Line(A, B)), 6);Equals(LengthOf(Line(C, D)), x);Equals(LengthOf(Line(B, C)), x+3);PointLiesOnLine(D, Line(A, C));Equals(MeasureOf(Angle(D, B, A)), MeasureOf(Angle(D, B, C))); |
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