Unlocking the Mystery of Inscribed Angles: A Complete Guide

Examples

Practice Questions:

1. In a circle, an inscribed angle intercepts an arc measuring \( 180^\circ \). What is the measure of the inscribed angle?
2. If an angle is inscribed in a semicircle, what is the measure of this angle?
3. Two inscribed angles intercept congruent arcs. If one angle measures \( 45^\circ \), what is the measure of the other angle?
4. An inscribed angle in a circle measures \( 30^\circ \). Find the measure of the intercepted arc.

1. \( 90^\circ \) (Since the inscribed angle is half the measure of the intercepted arc)
2. \( 90^\circ \) (An angle inscribed in a semicircle is always a right angle)
3. \( 45^\circ \) (Inscribed angles intercepting congruent arcs are congruent)
4. \( 60^\circ \) (The intercepted arc is twice the measure of the inscribed angle)