Question

question 5 of 10 if the measure of ∠xyz is 73°, what is the measure of ⁀xy? a. 36.5° b. 146° c. 107° d. 73°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc.
Let the measure of arc $XY$ be $m\overparen{XY}$. The inscribed angle $\angle XYZ = 73^{\circ}$.
According to the inscribed - angle formula $\angle XYZ=\frac{1}{2}m\overparen{XY}$.

Step2: Solve for the measure of arc $XY$

We can rewrite the formula as $m\overparen{XY} = 2\angle XYZ$.
Substitute $\angle XYZ = 73^{\circ}$ into the formula: $m\overparen{XY}=2\times73^{\circ}=146^{\circ}$.

Answer:

B. 146°