Answer: The measure of an inscribed angle with the center of the circle in the interior of the angle is half the measure of its intercepted arc.
In a circle, an inscribed angle is an angle formed by two intersecting chords of the circle, where the vertex of the angle lies on the circle. An intercepted arc is the arc that lies between the endpoints of the angle on the circle. The measure of an inscribed angle with the vertex on the center of the circle will always be half of the intercepted arc.
The reason for this is that an inscribed angle will always cut off an arc with the same measure as the angle itself. When the vertex of the inscribed angle is at the center of the circle, the two chords that form the angle will be diameters of the circle, and the intercepted arc will be the entire circumference of the circle. Since the circumference of a circle is always equal to 2π times the radius, and the radius of the circle is equal to half the diameter (which is the chord that forms the angle), the measure of the intercepted arc is twice the measure of the angle. Therefore, the measure of the angle is half of the measure of the intercepted arc.