Central Angles

1
Central Angles
2
Central Angle
An Angle whose vertex is at
the center of the circle
A
Minor Arc
Major Arc
More than 180
Less than 180
P
C
To name use 2 letters
To name use 3 letters
B
ltAPB is a Central Angle
3
Semicircle An Arc that equals 180
To name use 3 letters
E
D
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
http//www.mathopenref.com/linearpair.html
120
60
7
measure of an arc measure of central angle
A
E
96?
Q

96
B
C

264

84
8
Arc Addition Postulate
A
C
B
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Tell me the measure of the following arcs.
240?
A
D
140?
260?
m BCA
R
40?
100?
80?
C
B
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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
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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
INTERCEPTEDARC
INSCRIBEDANGLE
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Determine whether each angle is an inscribed
angle. Name the intercepted arc for the angle.
1.
14
Determine whether each angle is an inscribed
angle. Name the intercepted arc for the angle.
2.
Q
V
K
R
S
15
To find the measure of an inscribed angle
160
80
16
http//www.geogebra.org/en/upload/files/english/Gu
y/Circles_and_angles/Inscribed_Anlge.html
17
What do we call this type of angle?
What is the value of x?
What do we call this type of angle?
How do we solve for y?
The measure of the inscribed angle is HALF the
measure of the inscribed arc!!
120
x
y
18
http//www.geogebra.org/en/upload/files/english/Gu
y/Circles_and_angles/Inscribed_angle_practice.html
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Examples
3. If m JK 80?, find m ltJMK.
40 ?
4. If m ltMKS 56?, find m MS.
112 ?
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If two inscribed angles intercept the same arc,
then they are congruent.
72?
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http//www.geogebra.org/en/upload/files/english/Gu
y/Circles_and_angles/Inscribed_angle_practice.html
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Example 5 In ?J, mltA 5x and mltB 2x 9. Find
the value of x.
mltA mltB
5x 2x9
x 3
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Classwork

• Page 193 9-23
• Page 207 1-15

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Whatever is left is homework