Question

question 4 of 10 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, congruent chords subtend equal central angles.

Step2: Identify given congruent chords

Chord $\overline{XY}$ is congruent to chord $\overline{YZ}$.

Step3: Determine the central angles

$\angle XOY$ and $\angle YOZ$ are the central - angles subtended by chords $\overline{XY}$ and $\overline{YZ}$ respectively. Given $\angle XOY = 36^{\circ}$, since $\overline{XY}\cong\overline{YZ}$, then $\angle YOZ=\angle XOY = 36^{\circ}$.

Answer:

B. 36°