Inscribed Angle Theorem Worksheet

Inscribed Angle Theorem

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

What is an Inscribed Angle?

An inscribed angle is an angle formed by two chords in a circle that have a common endpoint on the circle. This common endpoint is the vertex of the inscribed angle.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

1. If the measure of an intercepted arc is 80 degrees, what is the measure of the inscribed angle that intercepts it?

2. An angle inscribed in a semicircle is always a:

3. The measure of a central angle is   the measure of its intercepted arc.

4. If two inscribed angles intercept the same arc, then they are  .

5. In the circle below, if arc AB measures 120 degrees, what is the measure of angle ACB?

6. A quadrilateral ABCD is inscribed in a circle. If angle A measures 70 degrees, what is the measure of angle C?

7. The measure of a central angle is always greater than the measure of an inscribed angle that intercepts the same arc.

8. All angles inscribed in the same arc are congruent.

9. Prove the Inscribed Angle Theorem for the case where one side of the inscribed angle is a diameter of the circle.