Warm-up

1
Adjacent Angles
Two angles are adjacent if they share a common
vertex and side, but have no common interior
points. SIDE BY SIDEshoulder to shoulder.
NO
YES
2
Linear Pairs
Two adjacent angles are a linear pair if their
noncommon sides are opposite rays. They form a
straight line SIDE BY SIDEshoulder to shoulder.
1
2
The sum of the measure s of angles that form a
linear pair is 180º
3
Please Identify in your notes all LINEAR PAIRS
i
m
e
j
k
h
f
g
4
SOME POSSIBLE ANSWERS
i
e
m
j
k
h
f
g
5
MORE POSSIBLE ANSWERS
i
m
e
j
k
h
f
g
6
1. Determine whether each statement is true or
false.
1
2
FALSE
7
2.
4
5
TRUE
8
3.
6
3
FALSE
9
C
4.
8
7
A
T
TRUE
10
C
5.
8
7
A
T
FALSE
11
Vertical Angles
Two angles are vertical angles if their sides
form two pairs of opposite rays
Vertical angles are always congruent.
Angles 1 and 2 are vertical angles
1
3
4
Angles 3 and 4 are also vertical angles
2
12
Identify all pairs of VERTICAL ANGLES
b
a
c
d
i
m
e
j
k
h
f
g
13
What is the measure of the angle?
5y -50
What type of angles are these?
4y-10
5y - 50 4y - 10
y 40
Plug y back into our angle equations and we get
14
Identify each pair of angles as adjacent,
vertical, and/or as a linear pair.
Example 1
ADJACENT
15
Identify each pair of angles as adjacent,
vertical, and/or as a linear pair.
Example 2
VERTICAL
16
Identify each pair of angles as adjacent,
vertical, and/or as a linear pair.
Example 3
ADJACENT
17
Identify each pair of angles as adjacent,
vertical, and/or as a linear pair.
Example 4
ADJACENT, LINEAR PAIR
18
Find x, y, and z.
Example 5
129, 51, 129
19
Example 6
Find x.
X 8
20
Example 7
Find
Since we have already found the value of x, all
we need to do now is to plug it in for ?LAT.
155
21
Supplementary Angles
Two angles are supplementary if the sum of their
measures is 180 degrees. Each angle is the
supplement of the other.
1
2
These are supplements of each other because their
angles add up to 180.
22
Example 1 Find the value of x.
23
Example 2 Find the value of x.
24
Example 3 Find the value of x.
25
Complementary Angles
Two angles are complementary if the sum of their
measures is 90 degrees. Each angle is the
complement of the other.
1
2
These are complements of each other because their
angles add up to be 90.
26
How can I remember the difference between
complementary and supplementary? Hmmm..
"Nice smile you over there in the second row."
"Great notes you in the front."
Its just nice to give people compliments.
Remember the sentence below and it will help
remind you that complementary angles are just the
ones that add up to a right angle.
A compliment is just right.
27
Example 4 Find the value of x.
28
Example 5 Find the value of x.
29
1
2
5
3
4
no
Are angles 1 and 2 a linear pair?
no
Are angles 1 and 3 adjacent angles?
yes
Are angles 3 and 4 a linear pair?
Are angles 2 and 3 adjacent angles?
yes
30
1
2
5
3
4
no
Are angles 4 and 5 supplementary angles?
no
Are angles 2 and 3 complementary angles?
Are angles 4 and 3 supplementary angles?
yes
Are angles 2 and 1 complementary angles?
yes