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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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 ° ° = 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