Question

question 5 of 10 what is the measure of ∠xyz?

Explanation:

Step1: Recall arc - angle relationship

The measure of an inscribed angle is half the measure of its intercepted arc. The measure of $\angle VYW$ is $\frac{44^{\circ}}{2}=22^{\circ}$ and the measure of $\angle XYZ$ and $\angle VYW$ are vertical angles. Also, the sum of the arcs of a circle is $360^{\circ}$. The arc $XWZ$ has measure $360-(44 + 86)=230^{\circ}$. The inscribed - angle $\angle XYZ$ intercepts arc $XWZ$.

Step2: Calculate $\angle XYZ$

The measure of an inscribed angle $\theta$ that intercepts an arc of measure $m$ is $\theta=\frac{m}{2}$. The arc intercepted by $\angle XYZ$ has measure $230^{\circ}$. So, $\angle XYZ=\frac{230^{\circ}}{2}=130^{\circ}$.

Answer:

C. $130^{\circ}$