Question

Explain the relationship between the measure of the inscribed angle and measure of the arc subtends it.​

Answer 1

—The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

The measure of an inscribed angle is half the measure of the intercepted arc. That is, m∠ABC=12m∠AOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.