Warm-Up Find the area of the shaded region. 10m 140°

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Presentation transcript:

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

Example Find each measure.

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

Theorem 3 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. A B C D

Example Find each angle measure.