Question

analyzing central and circumscribed angles
what is the measure of angle wzy?
○ 54.5°
○ 71°
○ 125.5°
○ 180°
109°

Explanation:

Step1: Find central angle ∠WXY

The total degrees in a circle is $360^\circ$. Subtract the given arc measure.
$\angle WXY = 360^\circ - 109^\circ = 251^\circ$

Step2: Apply circumscribed angle theorem

The measure of a circumscribed angle formed by two tangents is half the difference of the intercepted arcs.
$\angle WZY = \frac{1}{2} \times (251^\circ - 109^\circ)$

Step3: Calculate the final angle

Simplify the expression to find the angle measure.
$\angle WZY = \frac{1}{2} \times 142^\circ = 71^\circ$

Answer:

B. $71^\circ$