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Geometry
2.4 Special Pairs of Angles
In this lesson we will learn
about:
•Complimentary angles
•Supplementary angles
•Vertical angles
7
Complementary angles (Comp
‘s)
Two angles whose measures have the sum 90.
Each angle is called a complement of the other.
Y
.
.
W
.
Z
7
7
X
XYW is a complement of
WYZ
If an angle has a measure of x o,
What is the measure of its complement? o
90 - x
o
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Complementary angles (Comp
R
T are
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complementary
o
30
S
7
60
R and
o
T
‘s)
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Supplementary angles (Supp
‘s)
Two angles whose measures have the sum 180.
Each angle is called a supplement of the other.
D
7
DEG is a supplement of
GEF
E
G
F
If an angle has a measure of x o,
What is the measure of its supplement?
o
o
180 - x
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50
o
130
o
B
A
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A and
B are supplementary
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Supplementary angles (Supp
‘s)
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Example
A supplement of an angle is three times as large as
a complement of the angle. Find the measure of the
angle.
Let x = measure of the angle
Then 180 – x = the measure of its supplement
And 90 – x = the measure of its complement
180 – x
180 – x
2x
x
= 3 (90 – x)
= 270 – 3x
= 90
= 45
The angle is 45o and its complement is
90 – 45 = 45o and its supplement is
180 – 45 = 135o.
7
Vertical angles (Vert
‘s)
Two angles such that the sides of one angle are opposite
rays to the sides of the other angle. When two lines
intersect, they form two pairs of vertical angles.
Basically, fold an angle over its vertex to find
its vertical angle.
“V”ertical starts with a V, so fold the “V” down
to find its “V”ertical angle.
3 are vert
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2 and
7
4 are vert
7
7
3
4
7
2
1 and
7
1
‘s
‘s
In a proof, these will both work. You will never use Vertical Angles Defn.
Vertical Angles Thm.
Vertical angles are congruent.
7

3
1
2
‘s
2
Think:
What do you
know about the sum of the
measure of supplementary
‘s 1 and 3 ? The sum = 180
7
7
1
2 are vertical
7
7
7
Prove:
1 and
7
Given:
‘s 2 and 3 ?
The sum = 180
7
1 and
7
7
1
7

2 are vertical
7
Given:
Prove:
2
Statements
7
m
= 180
= 180
=m 2 + m
=
m
=m 2
3
3
Angle Add. Post
2.
Substitution
Reflexive
Subtr. POE
4.
3
1
1.
3.
7
4.
3
3
3
3
7
7
7
3.
1 + m
2 + m
1 + m
m
1
Reasons
7
7
7
2.
m
m
m
7
7
7
7
1.
‘s
2
Example
4

m
7
7
In this diagram, m
5
Name two other angles
congruent to
5.
9
7
8
7
4
5
6
7
8 because vertical angles are congruent(vert angles thm.)
7
7 by the Transitive Property (
m<7=m<4 and m<4=m<5
)
Homework
P.53 Let’s do #33 Together
P. 52 (1-33 Odd)
P. 57 (1-11 Odd)