Central Angle :
An Angle whose vertex is at the center of the circle
A
Major Arc
Minor Arc
More than 180°
Less than 180°
P
ACB
To name: use
3 letters
AB
C
B
<APB is a Central Angle
To name: use
2 letters
Semicircle: An Arc that equals 180°
E
D
To name: use
3 letters
EDF
P
F
EF is a diameter, so every diameter divides the
circle in half, which divides it into arcs of 180°
THINGS TO KNOW AND
REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
Linear Pairs are Supplementary
Vertical Angles are Equal
Linear Pairs are Supplementary
http://www.mathopenref.com/linearpair.html
120°
60°
measure of an arc = measure of central angle
A
E
Q
m AB = 96°
m ACB = 264°
m AE = 84°
96
B
C
Arc Addition Postulate
A
C
B
m ABC = m AB + m BC
Tell me the measure of the following arcs.
m DAB = 240
m BCA = 260
D
C
140
R
40
100
80
B
A
Congruent Arcs have the same measure and
MUST come from the same circle or from
congruent circles.
C
B
45
A
45
D
110
Classwork
• Page 193 #9-18
You have 15
minutes.
Inscribed Angle:
An angle whose
vertex
is on
the circle and
sides
are chords
whose
the circle
of
Determine whether each angle is an
inscribed angle. Name the intercepted
arc for the angle.
1.
C
T
O
L
YES;
CL
Determine whether each angle is an
inscribed angle. Name the intercepted
arc for the angle.
2.
Q

NO;
QVR
V
K

R

S
To find the measure of an inscribed angle…
Intercepte d Arc
Inscribed Angle 
2
160°
80°
http://www.geogebra.org
/en/upload/files/english/
Guy/Circles_and_angles/
Inscribed_Anlge.html
What
do
we
call
this
type
angle?
WhatWhat
do
How
weis
do
call
the
we
this
solve
value
type
for
ofof
of
x?
y?
angle?
The measure of the inscribed angle is HALF the
measure of the inscribed arc!!
120
x
y
http://www.geogebra.org/en/upload/fi
les/english/Guy/Circles_and_angles/I
nscribed_angle_practice.html
Examples
3. If m JK = 80, find m <JMK.
40 
4. If m <MKS = 56, find m MS.
112 
J
K
Q
M
S
If two inscribed angles intercept the
same arc, then they are congruent.
72
http://www.geogebra.org/en/upload
/files/english/Guy/Circles_and_ang
les/Inscribed_angle_practice.html
Example 5
In J, m<A= 5x and m<B = 2x + 9.
Find the value of x.
m<A = m<B
5x = 2x+9
x=3
Q
D
T
A
J
B
U
Classwork:
• Page 193 #9-23
• Page 207 #1-15
Whatever is left is homework