Question

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

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 inscribed angle $\angle Y$ intercepts arc $\overset{\frown}{XZ}$, and the measure of arc $\overset{\frown}{XZ}$ is $86^{\circ}$.

Step3: Calculate the measure of $\angle Y$

Using the inscribed - angle theorem, $m\angle Y=\frac{1}{2}m\overset{\frown}{XZ}$. Substituting $m\overset{\frown}{XZ} = 86^{\circ}$, we get $m\angle Y=\frac{86^{\circ}}{2}=43^{\circ}$.

Answer:

$43^{\circ}$