Question

If triangle BTS cong triangle GHD, BS = 25, TS = 14, BT = 31, GD = 4x - 11, m angle S = 56°, m angle B = 21°, and m angle H = (7v + 5)°, find the values of x and y.

A) x = 10, y = 5
B) x = 9, y = 7
C) x = 11, y = 6
D) x = 8, y = 4

Answer 1

To find the values of x and y, we can use the angle-angle-side (AAS) congruence criterion for triangles. Given that triangle BTS is congruent to triangle GHD, we know that angle B is congruent to angle H.

Step-by-step explanation:

To find the values of x and y, we can use the angle-angle-side (AAS) congruence criterion for triangles. Given that triangle BTS is congruent to triangle GHD, we know that angle B is congruent to angle H. Therefore, we can set up an equation: 21° = 7v + 5°. Solving for v, we find that v = 2. Then, we can substitute this value back into the expression for GD and solve for x:

GD = 4x - 11 = 4(2) - 11 = 8 - 11 = -3

Therefore, the values of x and y are x = -3 and y = 2.