10.4  Inscribed Angles

1. 10.4  Inscribed Angles

2. Intercepted arc inscribed angle inscribed angle  vertex is on the circle.  sides contain chords of the circle.

3. Intercepted arc inscribed angle Theorem:Measure of an inscribed angleIf an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc. = 64° 32°

4. 66° 66°

5. 54°

6. 43° 86° 43°

7. Intercepted arc inscribed angle Theorem: If two inscribed angles of a circle intercept the same arc, then the angles are congruent. = 64° 32° 32°

8. Find the measure in circle O: 74°

9. Find the measure in circle O: 132° 96°

10. Find the measure in circle O: 43.5°

11. Find the measure in circle O: 56°

12. Find the measure in circle O: 19° 38° 142°

13. Find the measure in circle O: 21° 138° 42°

14. inscribed If all the vertices of a polygon lie on a circle: the polygon is inscribed in the circle, and the circle is circumscribed about the polygon.

15. A B D C TheoremA quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

16. a. PQRS is inscribed in a circle, so opposite angles are supplementary. a. mQ + m S = 180o m P + m R = 180o EXAMPLE 5 Use Theorem 10.10 Find the value of each variable. SOLUTION 75o + yo = 180o 80o + xo = 180o y = 105 x = 100

17. b. JKLMis inscribed in a circle, so opposite angles are supplementary. b. mK + m M = 180o m J + m L = 180o EXAMPLE 5 Use Theorem 10.10 Find the value of each variable. SOLUTION 4bo + 2bo = 180o 2ao + 2ao = 180o 6b = 180 4a = 180 b = 30 a = 45

18. AssignmentPage 676-6773-26 all, 28, 30