Question

what is the measure of ∠y?
options: 43°, 68°, 86°, 172°
(there is a circle with points x, z, y on it. arc xz is 86°.)

Explanation:

Step1: Recall Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Here, $\angle Y$ intercepts arc $XZ$ which is $86^\circ$.

Step2: Calculate $\angle Y$

Using the theorem, $\angle Y = \frac{1}{2} \times \text{measure of arc } XZ$. So, $\angle Y = \frac{1}{2} \times 86^\circ = 43^\circ$.

Answer:

$43^\circ$ (corresponding to the option with $43^\circ$)