Question

Find the value of x and the measure of each angle

Answer 1

see explanation

Explanation:

since QR ≅ RS , the triangle is isosceles with base angles congruent, so

∠ Q = ∠ S , that is

8x - 17 = 5x + 1 ( subtract 5x from both sides )

3x - 17 = 1 ( add 17 to both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Then

∠ Q = 8x - 17 = 8(6) - 17 = 48 - 17 = 31°

∠ R = 19x + 4 = 19(6) + 4 = 114 + 4 = 118°

∠ S = 5x + 1 = 5(6) + 1 = 30 + 1 = 31°