Given that and , find the value of .
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:
Since and are both radii of the circle, is an isosceles triangle. Base angles of an isosceles triangle are congruent, so . Now use this fact, along with the fact that the sum of the measures of the interior angles of a triangle is , to find the measure of .
Thus, the value of is 34.