Question

given ⊙o below, if wx and yz are congruent, what is the measure of ∠yoz? 103° a. 206° b. 257° c. 103° d. 77°

Explanation:

Step1: Recall circle - angle property

In a circle, if two arcs are congruent, then the central angles that intercept them are congruent.

Step2: Identify the given arcs and angles

We are given that $\overset{\frown}{WX}$ and $\overset{\frown}{YZ}$ are congruent. $\angle WO X = 103^{\circ}$ and $\angle YOZ$ is the central - angle that intercepts $\overset{\frown}{YZ}$. Since $\angle WO X$ intercepts $\overset{\frown}{WX}$, and $\overset{\frown}{WX}\cong\overset{\frown}{YZ}$, then $\angle YOZ=\angle WO X$.

Answer:

C. $103^{\circ}$