Central Inscribed and Circumscribed Angles in Circles

This picture represents

• Three Semi-Circles

• Three Inscribed Angles

• Three Central Angles

• Three Intercepted Arcs

What is the value of x?

• 22

• 25

• 15

• 20

A circumscribed angle is ________ its intercepted arc.

• equal to

• half the measure of

• supplementary to

• not related to

An inscribed angle is ___________ its intercepted arc.

• equal to

• half the measure of

• supplementary to

• not related to

Find the measure of the indicated angle.

• 65°

• 130°

• 50°

• 90°

Find the measure of the indicated angle.

• 45°

• 90°

• 60°

• 135°

A circumscribed angle has its vertex ____________ the circle

• at the center of

• on

• outside

• inside

What formula would you use to find m<A?

• angle = 1/2 (arc + arc)

• angle = 1/2 (arc - arc)

• angle = 1/2(arc)

• circumscribed angle = 180 - central angle

Answer explanation

<A is an inscribed angle.
angle = 1/2(arc)

The sides of circumscribed angles are _________ to the circle.

<B is the circumscribed angle.

• tangent

• secant

• parallel

• perpendicular

Answer explanation

tangent = touches the circle at one point

What formula would you use to find m<1?

• angle = 1/2 (arc + arc)

• angle = 1/2 (arc - arc)

• angle = 1/2(arc)

• circumscribed angle = 180 - central angle

Answer explanation

<1 is created from the tangent line, m, and chord AB. 
angle = 1/2(intercepted arc)