1. Warm up 30  80  100  180  100  260 

2. Wheel of Formulas!!

3. Central Angle Angle = Arc

4. Inscribed Angle Angle where the vertex is ON the circle

5. Inscribed Angle

6. 160  80  The arc is twice as big as the angle!!

7. 120  x y Find the value of x and y.    120  60 

8. Examples 1. If m JK = 80  and  JMK = 2x – 4, find x. M Q K S J 2. If m  MKS = 56 , find m MS. x = 22 112 

9. 72˚ If two inscribed angles intercept the same arc, then they are congruent. Find the measure of  DOG and  DIG D O G I

10. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

11. Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY A B C D

12. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. diameter

13. Example 3 In  J, m  3 = 5x and m  4 = 2x + 9. Find the value of x. 3 Q D J T U 4 x = 3

14. 4x – 14 = 90 H K G N Example 4 In  K, GH is a diameter and m  GNH = 4x – 14. Find the value of x. x = 26

15. z y 110 85 110 + y =180 y = 70 z + 85 = 180 z = 95 Example 5 Find y and z.

16. Practice WS 10 problems

17. Homework WS 6.4 Practice