Question

question 7 of 10 given ⊙o below, if wx and yz are congruent, what is the measure of ∠yoz? 103° a. 206° b. 103° c. 257° d. 77°

Explanation:

Step1: Recall congruent - arc property

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

Step2: Identify given arcs and angles

We are given that $\widehat{WX}$ and $\widehat{YZ}$ are congruent. The central angle corresponding to $\widehat{WX}$ is $\angle WOX = 103^{\circ}$, and the central angle corresponding to $\widehat{YZ}$ is $\angle YOZ$.

Step3: Determine the measure of $\angle YOZ$

Since the arcs are congruent, $\angle YOZ=\angle WOX = 103^{\circ}$.

Answer:

B. 103°