10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.

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Presentation transcript:

10.4 Inscribed Angles 5/7/2010

Using Inscribed Angles 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.

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

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

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

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

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

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

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°

Example 68/2 = = 62 62/2 = = = = 180 Same as arc QP = = 248

Assignment Practice Workbook p. 193 (1-15)