1. Central Angles

2. <APB is a Central Angle
Central Angle : An Angle whose vertex is at the center of the circle A
Major Arc
Minor Arc
More than 180°
Less than 180°
ACB P AB
To name: use 3 letters C
To name: use 2 letters B
<APB is a Central Angle

3. Semicircle: An Arc that equals 180°
To name: use 3 letters E D
EDF P F
EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of 180°

4. THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
Linear Pairs are Supplementary

5. Vertical Angles are Equal

6. Linear Pairs are Supplementary
120°
60°

7. measure of an arc = measure of central angle
96 Q
m AB =
96° B C
m ACB =
264°
m AE =
84°

8. Arc Addition PostulateB
m ABC =
+ m BC
m AB

9. 240 260 m DAB = m BCA = Tell me the measure of the following arcs. D
140
260
m BCA = R
40
100
80 C B

10. CONGRUENT ARCS
Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles. C B D 45 45
110 A

11. Classwork
Page 193 #9-18
You have 15 minutes.

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

13. Determine whether each angle is an inscribed angle
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 1.
YES; CL C L O T

14. Determine whether each angle is an inscribed angle
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
NO; QVR 2. Q V K R S

15. To find the measure of an inscribed angle…
160°
80°

17. 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 inscribed arc!!
120 x y

19. 40  112  Examples 3. If m JK = 80, find m <JMK.
4. If m <MKS = 56, find m MS.
112  M Q K S J

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

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

23. Classwork:
Page 193 #9-23
Page 207 #1-15

24. Whatever is left is homework