Question

triangle wxy is isosceles. ∠ywx and ∠yxw are the base angles. \overline{yz} bisects ∠wyx. m∠xyz = (15x)°. m∠yxz = (2x + 5)°. what is the measure of ∠wyx?
○ 5°
○ 15°
○ 75°
○ 150°

Explanation:

Step1: Identify base angles

Base angles ∠YWX = ∠YXZ = (2x + 5)°

Step2: Relate angle bisector

YZ bisects ∠WYX, so ∠WYX = 2∠XYZ = 2(15x)° = 30x°

Step3: Sum of triangle angles

∠YWX + ∠YXZ + ∠WYX = 180°
(2x + 5) + (2x + 5) + 30x = 180

Step4: Solve for x

34x + 10 = 180
34x = 170
x = 5

Step5: Calculate ∠WYX

∠WYX = 30x = 30×5 = 150°

Answer:

D. 150°