Inscribed and Central Angle

Front

What is the definition of a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle and whose sides are radii that extend to the circumference.

Front

What is the relationship between a central angle and the arc it intercepts?

Back

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

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.

Front

How is the measure of an inscribed angle related to the arc it intercepts?

Back

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

Front

If the measure of arc AB is 68 degrees, what is the measure of the central angle that intercepts arc AB?

Back

68 degrees.

Front

If the measure of arc NM is 186 degrees, what is the measure of the inscribed angle that intercepts arc NM?

Back

93 degrees.

Front

In a circle, if angle CBA is 63 degrees, what is the measure of angle CQA (the angle opposite to CBA in an inscribed quadrilateral)?

Back

117 degrees.

Front

What is the formula to find the measure of an arc given the central angle?

Back

The measure of the arc is equal to the measure of the central angle.

Front

If the measure of arc AB is 34 degrees, what is the measure of the inscribed angle that intercepts arc AB?

Back

17 degrees.

Front

What is the sum of the measures of opposite angles in an inscribed quadrilateral?

Back

The sum of the measures of opposite angles in an inscribed quadrilateral is 180 degrees.