Question

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

Answer 1

Angle Y = 90° (XZ is a diameter). So angle Z = 180° − 90° − 59° = 31°. An inscribed angle equals half its intercepted arc, so arc XY = 2·∠Z = 2·31° = 62°.