Question

In the triangle shown, XY ≌ ZY and m∠Y = 38°. What is m∠Z?

A.35.5
B.38
c.71
d.142

Answer 1

c. 71°

Explanation:

You have isosceles triangle XYZ with a.pex angle Y = 38°. You want to know the measure of angle Z.

Angle sum theorem

The base angles of the triangle are X and Z, which are congruent. The sum of all angles is 180°:

X +Y +Z = 180°

2Z +38° = 180° . . . . . . substitute for X and Y

2Z = 142° . . . . . . . . . subtract 38°

Z = 71° . . . . . . . . . . divide by 2

The measure of angle Z is 71°.