Question

inscribed angle theorem
what is the measure of ∠y?
172°
43°
86°
68°

Explanation:

Step1: Recall inscribed - angle theorem

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

Step2: Identify the intercepted arc

The intercepted arc of ∠Y is arc XZ, which has a measure of 86°.

Step3: Calculate the measure of ∠Y

Let m∠Y be the measure of the inscribed angle. Using the inscribed - angle theorem, m∠Y=$\frac{1}{2}$× measure of arc XZ. So m∠Y = $\frac{1}{2}\times86^{\circ}=43^{\circ}$.

Answer:

43°