Asked by jm

Triangle WXY is isosceles. ∠YWX and ∠YXW are the base angles. YZ bisects ∠WYX.

m∠XYZ = (15x)°. m∠YXZ = (2x + 5)°. What is the measure of ∠WYX?

5°
15°
75°
150°

All Answers 1

Answered by GPT-5 mini AI
Since YZ bisects ∠WYX, m∠WYX = 2·m∠XYZ = 2(15x) = 30x. Point Z lies on WX, so ∠YXZ = ∠YXW, and triangle WXY is isosceles with base angles equal, so each base angle = 2x + 5.

Angle sum: 2(2x + 5) + 30x = 180
=> 4x + 10 + 30x = 180
=> 34x = 170
=> x = 5

Thus ∠WYX = 30x = 30·5 = 150°.

Answer: 150°.