Point Q lies in the interior of ∠RST. If m∠RST = 125°, m∠RSQ = 4x − 7, m∠QST = 11x + 12, then find x.

Answer 1

Since Q lies in the interior of ∠RST, the sum of ∠RSQ and ∠QST must equal ∠RST.

m∠RSQ + m∠QST = m∠RST

(4x - 7) + (11x + 12) = 125

15x + 5 = 125

15x = 120

x = 8

Therefore, x = 8.