Inscribed and Central Angle

Front

What is an inscribed angle in a circle?

Back

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

Front

What is the relationship between an inscribed angle and the arc it intercepts?

Back

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

Front

If an inscribed angle measures 45º, what is the measure of the intercepted arc?

Back

90º (because the arc is twice the angle).

Front

What is a central angle in a circle?

Back

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

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

If the measure of arc AB is 68º, what is the measure of the central angle AOB?

Back

68º (because the central angle is equal to the arc measure).

Front

What is the measure of angle ACB if arc AB is 68º?

Back

34º (because angle ACB is an inscribed angle and is half of arc AB).

Front

In a circle, if angle ABC is an inscribed angle measuring 45º, what is the measure of arc AC?

Back

90º (because the arc is twice the inscribed angle).

Front

What is the measure of arc AB if the inscribed angle ACB measures 34º?

Back

68º (because the arc is twice the inscribed angle).

Front

If quadrilateral ABCD is inscribed in a circle, what is the relationship between opposite angles?

Back

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