Inscribed AnglesInscribed Angles – An angle

that has its vertex on the circle and its sides contained in chords of the circle.

Intercepted – An angle intercepts an arc if and only if the following conditions are met:

1. The endpoints of the arc lie on the angle.

2. All points of the arc except the endpoints are in the interior of the angle.

3. Each side of the angle contains an endpoint of the arc.

A

B

C

D

Inscribed AnglesInscribed Angle Theorem• An inscribed angle is

equal in measure to half its intercepted arc.

Theorem 10.6• Inscribed angles that

intercept the same arc or congruent arcs are equal.

Theorem 10.7• An inscribed angle that

intercepts a semicircle is a right angle.

A

B

C

D

E

Inscribed Angles

Theorem 10.8

• If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

C

E

A

B

D

In and Find the measures of the numbered angles.

Answer:

Answer:

ALGEBRA Triangles MNO and MPO are inscribed in with Find the measure of each numbered angle if and

Answer:

Quadrilateral BCDE is inscribed in If and find and