1. Section 10.4 – Other Angle Relationships in Circles
Chapter 10 - Circles
Section 10.4 – Other Angle Relationships in Circles

2. Unit Goals
Use angles formed by tangents and chords to solve problems.

3. What Is the Measure of the Arc and Angle?

4. Theorem 10.12
If a tangent and chord intersect at a point on the circle, then the measure of each angle formed is ½ of the measure of its intercepted arc.

5. Example
Find the measure of the indicated arc or angle:
140º

6. Example
Find the value of x:

7. Theorem 10.13
If two chords intersect at a point in a circle, then the measure of each angle formed is ½ the sum of the measures of the intercepted arcs.

8. Example
Find the measure of the indicated angle:
20º
70º

9. Example
Find the measure of the indicated angle:
90º
150º

10. Theorem 10.14
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle is ½ the difference of the intercepted arcs.

11. Example
Find the measure of the indicated angle:
94º
50º

12. Example
Find the measure of the indicated angle:
130º
230º

13. Example
Find the measure of the indicated angle:
190º
110º