Central and Inscribed Angles Review

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle and whose sides (rays) extend to the circumference of the circle.

Front

What is an inscribed angle?

Back

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

Front

How do you find the measure of a central angle?

Back

The measure of a central angle is equal to the measure of the arc it intercepts.

Front

How do you find the measure of an inscribed angle?

Back

The measure of an inscribed angle is half the measure of the arc it intercepts.

Front

If the measure of an arc is 150°, what is the measure of the inscribed angle that intercepts it?

Back

75° (because the inscribed angle is half of the arc measure).

Front

If the measure of a central angle is 205°, what is the measure of the arc it intercepts?

Back

205° (the measure of the central angle is equal to the measure of the arc).

Front

What is the relationship between the measures of a central angle and its intercepted arc?

Back

The measure of a central angle is equal to the measure of the arc it intercepts.

Front

What is the relationship between the measures of an inscribed angle and its intercepted arc?

Back

The measure of an inscribed angle is half the measure of the arc it intercepts.

Front

Solve for x if the inscribed angle is 12x and the intercepted arc is 72°.

Back

x = 3 (since 12x = 72, x = 72/12).

Front

If an inscribed angle measures 52°, what is the measure of the intercepted arc?

Back

104° (because the intercepted arc is twice the inscribed angle).