gen-define-the-inscribed-angle-theorem-and-give-one-short-worked-a547

Define the inscribed angle theorem and give one short worked example.

# Inscribed Angle Theorem **Definition:** An inscribed angle is formed by two chords that share an endpoint on a circle. The **Inscribed Angle Theorem** states that an inscribed angle is half the measure of the central angle that subtends the same arc. Equivalently: An inscribed angle equals half the measure of its intercepted arc. ## Worked Example **Problem:** In a circle, an inscribed angle intercepts an arc of 80°. What is the measure of the inscribed angle? **Solution:** Using the Inscribed Angle Theorem: Inscribed angle = ½ × (intercepted arc) Inscribed angle = ½ × 80° = **40°** --- **Visual note:** If the same arc is subtended by a central angle (vertex at the center), that central angle would measure 80°, while any inscribed angle on the circle intercepting the same arc would measure 40°.