What is the measure of an inscribed angle in relation to its intercepted arc?

An inscribed angle is defined as an angle formed by two chords in a circle that share an endpoint. This angle intercepts an arc, which is the part of the circle that lies between the two points where the chords meet the circle. The measure of the inscribed angle is always half the measure of the intercepted arc.

This relationship holds because the inscribed angle subtends the arc and its measure is dependent on that arc. If you were to measure the angle in degrees, you would find that it is precisely half of the degrees of the arc that it intercepts. This fundamental property of circles is derived from the cyclic nature of angles formed by points on a circumference.

So, when considering the measure of an inscribed angle in relation to its intercepted arc, one can confidently state that the measure of the inscribed angle is one half the measure of its intercepted arc.