1. 9.4 Inscribed Angles Geometry

3. Objectives/Assignment Use inscribed angles to solve problems. Use properties of inscribed polygons.

4. Review

5. Definitions An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. The arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the intercepted arc of the angle.

6. Theorem 9.4: Measure of an Inscribed Angle m  ADB = ½m

7. Finding Measures of Arcs and Inscribed Angles Find the measure of the blue arc or angle. m = 2m  QRS = 2(90°) = 180°

8. Finding Measures of Arcs and Inscribed Angles Find the measure of the blue arc or angle if  ZYX = 115 °. m = 2m  ZYX 2(115°) = 230°

9. Finding Measures of Arcs and Inscribed Angles Find the measure of the blue arc or angle. m = ½ m ½ (100°) = 50° 100°

10. Theorem 9.5  C   D

11. Comparing Measures of Inscribed Angles Find m  ACB, m  ADB, and m  AEB if AB = 60 °. The measure of each angle is half the measure of m = 60°, so the measure of each angle is 30°

12. Finding the Measure of an Angle Given m  E = 75 °. What is m  F?  E and  F both intercept, so  E   F. So, m  F = m  E = 75° 75°

13. Find x. AB is a diameter. So,  C is a right angle and m  C = 90 ° 2x° = 90° x = 45 2x°

14. ½ * 96 = (2x + 1) 48 = 2x + 1 47 = 2x X = 23.5 m PQR = ½ m PR

15. x = 2x – 3 - x = -3 X = 3

16. m  P = 90 ½ x + (1/3 x +5) = 90 5/6 x + 5 = 90 5/6 x = 85 X = 102

17. Practice