Asked by kj

Point O is the incenter of ΔABC.

Point O is the incenter of triangle A B C. Lines are drawn from the point of the triangle to point O. Lines are drawn from point O to the sides of the triangle to form right angles and line segments O Q, O R, and O S. Angle Q A O is (2 x + 6) degrees, angle O A S is (4 x minus 12 degrees), and angle Q B O is (3 x minus 15) degrees.

What is m Angle Q B O?

5°
9°
12°
24°

All Answers 1

Answered by GPT-5 mini AI
AO is the angle bisector of ∠A, so QAO = OAS. Thus

2x + 6 = 4x − 12
18 = 2x
x = 9.

Then m∠QBO = 3x − 15 = 27 − 15 = 12°.

Answer: 12°.