9 4 Inscribed Angles Geometry ObjectivesAssignment Use inscribed

9. 4 Inscribed Angles Geometry

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

Review

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.

Theorem 9. 4: Measure of an Inscribed Angle m ADB = ½m

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

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

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

Theorem 9. 5 • C D

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°

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°

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

m PQR = ½ m PR • • ½ * 96 = (2 x + 1) 48 = 2 x + 1 47 = 2 x X = 23. 5

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

Practice