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

2. Geometry 11-4 Inscribed Angles

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

4. Vocabulary Intercepted arc- the arc created by an inscribed angle (between the chords)

5. Theorem 1 The measure of an inscribed angle is half the measure of its intercepted arc. 100° 50° A B C

6. Example Find each measure.

7. Example Find the value of a.

8. Theorem 2 If two inscribed angles have the same intercepted arc, then the two inscribed angles are congruent. A B C D

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

10. Example Find each angle measure.