Triangle XYZ

Question

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 a circle with diameter XZ, angle Y is an inscribed angle and the measure of the arc that it intercepts is equal to twice the measure of the inscribed angle.

Therefore, the arc measure of XY is 2 * 59° = 118°.