1. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle
INTERCEPTED ARC
INSCRIBED ANGLE

2. What do we call this type of angle? What is the value of x?
How do we solve for y?
The measure of the inscribed angle is HALF the measure of the intercepted arc!!
120 x y

3. 40  112  Examples M Q K S J 1. If m JK = 80, find m  JMK.
2. If m MKS = 56, find m MS.
112 

4. 3. Find the measure of arc AL. (think about it!)
48º A

5. If two inscribed angles intercept the same arc, then they are congruent.
72

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

7. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
180
diameter

8. Example 5
In K, GH is a diameter and m  GNH = 4x – 14. Find the value of x.
4x – 14 = 90 H K
x = 26 N G

9. Example 6
In K, m  1 = 6x – 5 and m2  = 3x – 4. Find the value of x.
6x – 5 + 3x – 4 = 90 H 2 K
x = 11 1 N G

10. A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary. B A D C

11. y = 64 z = 95 110 + y+6 =180 z + 85 = 180 Example 7 Find y and z. z

12. Homework: Pg
1-20 all!