Question

Triangle W Z Y is cut by bisector Z X. The lengths of sides Z W and Z Y are congruent.
ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°, what is the value of m?

6
17
90
102

Answer 1

ZW = ZY so triangle WZY is isosceles, hence base angles at W and Y are equal. Let ∠WZY = θ, so each base angle = (180 − θ)/2 = 90 − θ/2. ZX bisects ∠WZY, so in triangle ZXY the angles are θ/2, 90 − θ/2, and ∠YXZ = 6m − 12. Sum to 180:

θ/2 + (90 − θ/2) + (6m − 12) = 180
90 + 6m − 12 = 180
6m + 78 = 180
6m = 102
m = 17

Answer: 17.