Interior and Exterior Angles Formed by Chords, Secants, and Tangents Lesson 10-6

Interior Angle Theorem Definition: Angles that are formed by two intersecting chords. 1 A B C D AEC and DEB are interior angles 2 E Interior Angle Theorem: The measure of the angle formed by the two intersecting chords is equal to ½ the sum of the measures of the intercepted arcs. Chapter 10-6: Interior and Exterior Angles

Chapter 10-6: Interior and Exterior Angles Example: Interior Angle Theorem 91 A C x° y° B D 85 Chapter 10-6: Interior and Exterior Angles

Chapter 10-6: Interior and Exterior Angles An angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle. 3 y ° x 2 1 Two secants 2 tangents A secant and a tangent Chapter 10-6: Interior and Exterior Angles

Exterior Angle Theorem The measure of the angle formed is equal to ½ the difference of the intercepted arcs. Chapter 10-6: Interior and Exterior Angles

Example: Exterior Angle Theorem mACB = ½ (mADB – mAB) mACB = ½ (265° - 95°) mACB = ½ (170) mACB = 85 D Chapter 10-6: Interior and Exterior Angles

Chapter 10-6: Interior and Exterior Angles Given AF is a diameter, mAG = 100°, mCE = 30°, and mEF = 25°. Find the measure of all numbered angles. m1 = mFG = 80° m 2 = mAG = 100° m 3 ½ (mCE + mEF) = = 27.5° m 4 ½ (mGF + mACE) = = 117.5° m 5 = 180 ° - 117.5 ° = 62.5 ° m 6 = ½ (mAG – mCE) = = 35° Q G F D E C 1 2 3 4 5 6 A 30° 25° 100° Chapter 10-6: Interior and Exterior Angles