Question

question 3 of 10
what is the measure of overline{xz}?
a. 36°
b. 72°
c. 108°
d. 144°

Explanation:

Step1: Recall inscribed angle theorem

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

Step2: Relate angle to arc

Given $\angle XYZ = 72^\circ$, it intercepts arc $XZ$. Let $m\overset{\frown}{XZ}$ be the measure of arc $XZ$.
$$m\angle XYZ = \frac{1}{2}m\overset{\frown}{XZ}$$

Step3: Solve for arc measure

Rearrange to solve for $m\overset{\frown}{XZ}$:
$$m\overset{\frown}{XZ} = 2 \times m\angle XYZ = 2 \times 72^\circ$$

Answer:

D. $144^\circ$