Question

50 angle y is inscribed in the circle below. the measure of arc xz is 205°. what is the measure of angle y? 77.5 °

Explanation:

Step1: Find the measure of the minor arc XZ

The total degrees in a circle is \(360^\circ\). The major arc XZ is \(205^\circ\), so the minor arc XZ is \(360^\circ - 205^\circ = 155^\circ\).

Step2: Use the inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. So angle Y, which intercepts arc XZ (minor arc), has a measure of \(\frac{1}{2} \times 155^\circ = 77.5^\circ\).

Answer:

\(77.5^\circ\)