and
Objective: Find the measures
of central angles and arcs.
A CIRCLE is the set of all
points equidistant from a given
point called the center.
This is circle P for Pacman.
Circle P
P
A CENTRAL ANGLE of a circle
is an angle with its vertex at
the center of the circle.
Central angle
An arc is a part of a circle. In
this case it is the part Pacman
would eat. 
Arc
One type of arc, a semicircle,
is half of a circle.
C
Semicircle ABC
m ABC = 180
P
A
B
A minor arc is smaller than
a semicircle. A major arc is
greater than a semicircle.
RS is a minor arc.
mRS = m RPS.
360 – mLN
R
N
S
P
LMN is a
major arc.
mLMN =
M
O
L
Identify the following in circle O:
1) the minor arcs
C
A
O
D
E
Identify the following in circle O:
2) the semicircles
C
A
O
D
E
Identify the following in circle O:
3) the major arcs containing
point A
C
A
O
D
E
The measure of a central
angle is equal to its
intercepted arc.
R
53o
53o
O
P
Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC = 180
4. AB = 148
Here is a circle graph that shows
how people really spend their
time. Find the measure of each
central angle in degrees.
1. Sleep
2. Food
3. Work
4. Must Do
5. Entertainment
6. Other
Homework:
page 569 (1 – 26)