Practice Inscribed Angle in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An angle whose vertex lies on the circle and whose sides are chords of the circle. Its measure is exactly half the measure of the intercepted arc.
Imagine sitting on the edge of a circular stadium and looking at two players on the field. The angle your eyes make is an inscribed angle. No matter where you sit on the same arc, that viewing angle stays the same—and it's always half of what you'd see from the center. It's like the circle is 'halving' your perspective compared to the center's view.
Example 1
easyAn inscribed angle intercepts an arc of 80°. What is the measure of the inscribed angle?
Example 2
mediumIn circle O, inscribed angle \angle ABC intercepts arc AC. If arc AC = 134°, and arc CD = 70°, find inscribed angle \angle ADC that intercepts arc AC from the same side.
Example 3
easyAn inscribed angle measures 35°. What is the measure of its intercepted arc?
Example 4
hardQuadrilateral ABCD is inscribed in a circle. If \angle A = 82°, find \angle C. Then, if arc AB = 96° and arc BC = 110°, find \angle ADC.