Recall that the measure of an arc of a circle is the same as the measure of its corresponding central angle. (See applet.)
Definition: An INSCRIBED ANGLE of a circle is an angle whose vertex lies on the circle and has each of its rays intersect the circle at one other point. (Click checkbox to show inscribed angle.)
Notice how both the inscribed angle and central angle both intercept the same arc.
Click on the CHECK THIS OUT !!! checkbox that appears afterwards. Be sure to move points A, B, and the pink vertex of the inscribed angle around. (You can also change the radius of the circle if you wish.)
In a circle, what is the relationship between the measure of an inscribed angle with respect to the measure of its intercepted arc?

Key directions and question are located above the applet.