Question

Triangle XYZ is inscribed 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. m XY=_degrees.

Answer 1

XZ is a diameter, so angle Y is a right angle (90°). With angle X = 59°, angle Z = 180° − 90° − 59° = 31°.
An inscribed angle measures half its intercepted arc, and angle Z intercepts arc XY, so m(arc XY) = 2·31° = 62°.