Warm-Up

• Find the area of the shaded region.

10m

140°

Geometry 11-4

Inscribed Angles

Vocabulary

• Inscribed angle- an angle whose vertex is on the circle and whose sides are chords.

Vocabulary

• Intercepted arc- the arc created by an inscribed angle (between the chords)

Theorem 1

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

100°

50°

A

B

C

12

m ABC AC

Example

• Find each measure.

m PRUPS

Example

• Find the value of a.

Theorem 2

• If two inscribed angles have the same intercepted arc, then the two inscribed angles are congruent.

A

B

C

D m ABC m ADC

Theorem 3

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

180A C

AB

C

D

180B D

Example

• Find each angle measure.