Central and Inscribed Angles

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.

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 calculate 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 calculate 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 arc AB is 80 degrees, what is the measure of the inscribed angle ACB?

Back

The measure of angle ACB is 40 degrees.

Front

What is the relationship between a central angle and an inscribed angle that intercept the same arc?

Back

The central angle is twice the measure of the inscribed angle.

Front

If m∠AOB = 100 degrees, what is the measure of arc AB?

Back

The measure of arc AB is also 100 degrees.

Front

If m∠PTQ = 70 degrees, what is the measure of arc PQ?

Back

The measure of arc PQ is 140 degrees.

Front

What is the formula for finding the measure of an arc in a circle?

Back

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

Front

If the measure of arc XY is 150 degrees, what is the measure of the central angle XOY?

Back

The measure of central angle XOY is 150 degrees.