Question

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

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc. Let the measure of the inscribed angle $\angle XYZ = 73^{\circ}$ and the measure of the intercepted arc be $\overset{\frown}{XY}$.

Step2: Apply the formula

If $\theta$ is the measure of the inscribed angle and $s$ is the measure of the intercepted arc, then $\theta=\frac{1}{2}s$. Given $\theta = 73^{\circ}$, we can solve for $s$. Rearranging the formula gives $s = 2\theta$.

Step3: Calculate the measure of the arc

Substitute $\theta = 73^{\circ}$ into the formula $s = 2\theta$. So, $s=2\times73^{\circ}=146^{\circ}$.

Answer:

B. $146^{\circ}$