Question

question 6 of 10 what is the measure of ∠z? a. 36° b. 144° c. 18° d. 72°

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 inscribed angle $\angle XYZ = 36^{\circ}$, and the arc it intercepts is arc $XZ$. Let the measure of arc $XZ$ be $m\overset{\frown}{XZ}$. According to the inscribed - angle theorem, $\angle XYZ=\frac{1}{2}m\overset{\frown}{XZ}$.

Step3: Solve for the measure of the arc

If $\angle XYZ = 36^{\circ}$, then $m\overset{\frown}{XZ}=2\times\angle XYZ$. So $m\overset{\frown}{XZ}=2\times36^{\circ}=72^{\circ}$.

Answer:

D. $72^{\circ}$