Question

what is the measure of $angle y$, in degrees?
a. $116^circ$
b. $64^circ$
c. cannot be determined
d. $32^circ$

Explanation:

Step1: Identify triangle type

Triangle XYZ has XY = ZY = 4, so it is isosceles with base angles $\angle X = \angle Z$.

Step2: State base angle measure

$\angle Z = \angle X = 32^\circ$

Step3: Sum angles to find $\angle Y$

Sum of triangle angles is $180^\circ$. So $\angle Y = 180^\circ - 32^\circ - 32^\circ$
$\angle Y = 180^\circ - 64^\circ = 116^\circ$

Answer:

A. $116^\circ$