1. Apply Other Angle Relationships in Circles
Lesson 10-5
Apply Other Angle Relationships in Circles

2. Angles Inside the Circle Theorem (Interior Angle Theorem)
Definition:
Angles that are formed by two intersecting chords. 1 A B C D 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.

3. Example: Interior Angle Theorem
91 A C x° y° B D
85

4. Practice: 1) 2)

5. 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

6. Angles Outside the Circle Theorem (Exterior Angle Theorem)
The measure of the angle formed is equal to ½ the difference of the intercepted arcs.

7. Example: Exterior Angle Theorem

8. Q G F D E C 1 2 3 4 5 6 A
30°
25°
100°

9. Practice: 1) 2)

10. An Angle Formed by a Chord and a Tangent
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

11. Practice: 1) 2)