1. Warm up NL and KM are diameters.
30
80
100
180
100
260

2. Review HW

3. Skills Check

4. Inscribed Angles and Inscribed Quadrilaterals

5. Wheel of Formulas!!

6. Central Angle
Angle = Arc

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

8. Inscribed Angle

9. 160
The arc is twice as big as the angle!!
80

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

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

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

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

14. Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY

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

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

17. Example 4
In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
4x – 14 = 90 H K G N
4x = 104
x = 26

18. Example 5 Solve for x and z.85
2x x – 6 = 180
24x +12 = 180
22x – 6
24x = 168
x = 7
z + 85 = 180
z = 95

19. CW / HW
Practice Workhseet