Given that , determine .
The measure of an inscribed angle of a circle is half the measure of the central angle subtended by the same arc. This means that the measure of is half the measure of . First, use this fact to find the measure of as follows:
A line segment that passes through the centre of a circle and is perpendicular to a chord of the circle bisects that chord. This means that bisects since and are both radii of the circle. Both and are right-angled triangles, so the sine of is equal to the sine of . This means that the measure of must be equal to the measure of . Use this fact, along with the fact that , to find the measure of .