Question

if chord $overline{xy}$ is congruent to chord $overline{yz}$, what is the measure of $angle yoz$? a. $54^{circ}$ b. $36^{circ}$ c. $72^{circ}$ d. $126^{circ}$

Explanation:

Step1: Recall circle - chord property

In a circle, if two chords are congruent, then the central angles subtended by them are congruent.

Step2: Identify given central angle

We know that $\angle XOY = 36^{\circ}$, and chord $\overline{XY}\cong$ chord $\overline{YZ}$. So, $\angle XOY=\angle YOZ$.

Answer:

B. $36^{\circ}$