1. Lesson 9-6 Other Angles (page 357) Essential Question How can relationships in a circle allow you to solve problems involving angles of a circle?

2. The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs. Theorem 9-9 B A C D 1

3. Here is why … just so you know! B A C D 1 2 3

4. The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs. B A C D 1

5. Example #1 S Q P R 1 45º 75º 60º

6. Example #2 S Q P R 1 55º 80º 30º

7. The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs. Theorem 9-10

8. 1 xº yº Case I: 2 secants

9. 1 xº yº I will show you why for Case I. 2 3

10. Theorem 9-10 2 xº yº Case II: 2 tangents

11. Theorem 9-10 3 xº yº Case III: secant & tangents

12. Example #3 B D C E A 100º 40º 30º

13. Example #4 X Y V Z W 65º 70º 200º

14. Example #5 Q R S P 240º 120º 60º

15. Worksheet on Lesson 9-6 Other Angles How can relationships in a circle allow you to solve problems involving angles of a circle? GRADED Assignment Written Exercises on pages 359 & 360 1 to 10 ALL numbers (make the diagram)

16. BEWARE! The next slide has the answers to the homework problems 1 to 10.

17. Page 359 #’s 1 to 10 90º 30º 20º 90º 25º 65º 55º 125º 35º 60º 90º60º 130º 90º