Question

if $\angle xyz$ and $\angle zyc$ form a linear pair and the measure of $\angle xyz$ is $36^\circ$, what is the measure of $\angle zyc$ ?
a. $36^\circ$
b. $54^\circ$
c. $144^\circ$
d. $63^\circ$

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). Let \(\angle XYZ = 36^\circ\) and \(\angle ZYC\) (assuming a typo, should be \(\angle ZYC\) or \(\angle ZYX\)? Wait, the question has \(\angle ZYC\) but likely a typo, but using linear pair: \(\angle XYZ + \angle ZYC = 180^\circ\).

Step2: Calculate \(\angle ZYC\)

Substitute \(\angle XYZ = 36^\circ\) into the equation: \(\angle ZYC = 180^\circ - 36^\circ = 144^\circ\).

Answer:

C. \(144^\circ\)