Triangle XYZ is inscribed inside a circle with diameter XZ and the inscribed angle at Y . The angle measure at X is 59°. Using what you know about inscribed angles, find the arc measure of XY

Answer 1

Since triangle XYZ is inscribed inside the circle with diameter XZ, we know that angle Y is an inscribed angle.

By the inscribed angle theorem, the measure of an inscribed angle is equal to half the measure of its intercepted arc.

Since angle X is 59°, the intercepted arc XY is twice that measure: 2 * 59° = 118°.

Therefore, the arc measure of XY is 118°.