Ray QS bisects ∠PQR, m∠PQR = (4x + 2)°, m∠SQR = (3x – 6)°. What is the value of x?

Answer 1

Since QS is an angle bisector, it cuts angle PQR exactly in half into two congruent angles, PQS and SQR. Each of these two angles is exactly one half as big as angle PQR. So:

m∠PQR = 2·m∠SQR

4x + 2 = 2·(3x-6)

Solve for x.