Question

6.4.3 quiz: congruent chords and circle angle measure
question 4 of 10
if chord $overline{xy}$ is congruent to chord $overline{yz}$, what is the measure of $angle yoz$?
a. 126°
b. 72°
c. 36°
d. 54°

Explanation:

Step1: Recall circle - chord property

In a circle, congruent chords subtend equal central angles.

Step2: Identify given angles

Since chord $\overline{XY}$ is congruent to chord $\overline{YZ}$, and $\angle XOY = 36^{\circ}$, then $\angle YOZ=\angle XOY$.
So, $\angle YOZ = 36^{\circ}$.

Answer:

C. 36°