2. _____________: An angle whose vertex is on the circle and whose sides are chords of the circle
INTERCEPTED ARC

3. Determine whether each angle is an inscribed angle
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 1. C L O T

4. Determine whether each angle is an inscribed angle
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 2. Q V K R S

5. To find the measure of an inscribed angle…
1600 ?

6. What do we call this type of angle?
The measure of the inscribed angle is HALF the measure of the inscribed arc!!
120
What is the value of x?...y? x y

7. Examples
3. If m JK = 80, find m <JMK.
4. If m <MKS = 56, find m MS. M Q K S J

8. If two inscribed angles intercept the same arc, then they are congruent.
720

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

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

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

12. Example 8 Find y and z. z
110 y 85

13. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
1800
diameter

14. Example 6
In K, m<GNH = 4x – 14. Find the value of x. H K N G

15. Example 7
In K, m<1 = 6x – 5 and m<2 = 3x – 4. Find the value of x. H 2 K 1 N G