Question

analyzing central and circumscribed angles what is the measure of angle wzy? 54.5° 71° 125.5° 180°

Explanation:

Step1: Recall the property of circumscribed - central angle

The measure of a circumscribed angle is supplementary to the measure of the central angle that subtends the same arc.

Step2: Identify the central angle

The central angle $\angle{WXY}$ is given as $109^{\circ}$.

Step3: Calculate the measure of $\angle{WZY}$

Let $\theta=\angle{WZY}$. Since $\theta + 109^{\circ}=180^{\circ}$ (circumscribed - central angle relationship), then $\theta=180^{\circ}- 109^{\circ}=71^{\circ}$.

Answer:

$71^{\circ}$