Question

question 7 of 10 what is the measure of ∠xyz?

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arc

The arc intercepted by $\angle XYZ$ is the arc $XZ$. The measure of the arc $XZ$ is $186^{\circ}$.

Step3: Calculate the measure of $\angle XYZ$

Let $m\angle XYZ=\theta$. According to the inscribed - angle theorem, $\theta=\frac{1}{2}\text{ (measure of arc }XZ)$. So, $\theta = \frac{1}{2}\times186^{\circ}=93^{\circ}$.

Answer:

B. $93^{\circ}$