Inscribed and Central Angle

Front

What is an inscribed angle?

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 the chords.

Front

What is a central angle?

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 an inscribed angle and the arc it intercepts?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Front

If the measure of arc AB is 68º, what is the measure of the inscribed angle that intercepts arc AB?

Back

34º (because the inscribed angle is half of the arc measure).

Front

What is the relationship between opposite angles in a cyclic quadrilateral?

Back

The opposite angles of a cyclic quadrilateral are supplementary, meaning they add up to 180º.

Front

If angle CBA is 63º in a cyclic quadrilateral, what is the measure of angle ACD?

Back

117º (because opposite angles are supplementary: 180º - 63º = 117º).

Front

How do you find the measure of an arc given the inscribed angle?

Back

Multiply the measure of the inscribed angle by 2 to find the measure of the intercepted arc.

Front

What is the formula for the measure of a central angle?

Back

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

Front

If the measure of arc NM is 186º, what is the measure of the central angle that intercepts arc NM?

Back

186º (because the central angle is equal to the arc measure).

Front

What is the sum of the measures of the angles in a quadrilateral?

Back

The sum of the measures of the angles in a quadrilateral is 360º.