Unlocking the Mystery of Inscribed Angles: A Complete Guide

An inscribed angle has its vertex on the circle and measures half the arc it intercepts. Two inscribed angles catching the same arc are therefore equal, whatever their positions on the circle.

Worked examples: inscribed angles

Practice questions on inscribed angles

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)

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