Key Concepts: Inscribed Angles

Inscribed Angle Theorem

An inscribed angle has its vertex on the circle. Its measure is half the measure of its intercepted arc.

m∠inscribed = ½ × m(intercepted arc)

Corollaries

• Inscribed angles that intercept the same arc are congruent.
• An inscribed angle that intercepts a semicircle is a right angle (90°).
• If a quadrilateral is inscribed in a circle, opposite angles are supplementary.