10.4 Inscribed Angles

1. 10.4 Inscribed Angles 5/7/2010

2. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. Intercepted arc is an arc that lies in the interior of an inscribed angle and has endpoints on the angle. Using Inscribed Angles

3. To find the measure of an arc use the central angle. 115˚ Central angle 115˚

4. Theorem 10.7: Measure of an Inscribed Angle A 130˚ • If an angle is inscribed in a circle, then its measure is one half the measure of its intercepted arc. mADB = ½m (½)130 = 65˚ B D

5. m = 2mQRS = 2(90°) = 180° Ex. 1: Finding Measures of Arcs and Inscribed Angles • Find the measure of the blue arc or angle.

6. Ex. 2: Finding Measures of Arcs and Inscribed Angles • Find the measure of the blue arc or angle. m = 2mZYX = 115˚ 2(115°) = 230°

7. Ex. 3: Finding Measures of Arcs and Inscribed Angles • Find the measure of the blue arc or angle. 100° m = ½ m ½ (100°) = 50°

8. If two inscribed angles of a circle intercept the same arc, then the angles are congruent. C  D Theorem 10.8

9. Ex. 4: Finding the Measure of an Angle • It is given that mE = 75°. What is mF? • E and F both intercept , so E  F. So, mF = mE = 75° 75°

10. Example 68/2 = 34 62/2 = 31 180-118 = 62 62 + 68 = 130 180-68 = 118 118 + 62 = 180 Same as arc QP =62 68 + 62 + 118 = 248

11. Assignment • Practice Workbook p. 193 (1-15)