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Two angles are adjacent if they share a common vertex and side, but have no common interior points. SIDE BY SIDE…shoulder to shoulder.
YES
NO
Two adjacent angles are a linear pair if their noncommon sides are opposite rays. They form a straight line… SIDE BY SIDE…shoulder to shoulder.
1 2
The sum of the measure s of angles that form a linear pair is 180º
j
im
k h f
e
g
Please Identify in your notes all LINEAR PAIRS
j
im
k h f
e
g
SOME POSSIBLE ANSWERS
j
im
kh f
e
g
MORE POSSIBLE ANSWERS
1 2
1. Determine whether each statement is true or false.
pair.linear a form 2 and 1
4 5
2.
pair.linear a form 5 and 4
63
3.
angles.adjacent are 3 and 6
87
4.
angles.adjacent are 8 and 7
C
A T
87
5.
angles.adjacent are 7 and CAT
C
A T
Two angles are vertical angles if their sides form two pairs of opposite rays
Angles 1 and 2 are vertical angles 1
2
3 4Angles 3 and 4 are also vertical angles
Vertical angles are always congruent.
a b
cd
j
im
k
h f
e
g
Identify all pairs of VERTICAL ANGLES
5y -50
4y-10
What type of angles
are these?
5y - 50 = 4y - 10y = 40
Plug y back into our angle equations and we get
150
What is the measure of the angle?
1
23
4
5
Identify each pair of angles as adjacent, vertical, and/or as a linear pair.
Example 1:
1 and 2
ADJACENT
Identify each pair of angles as adjacent, vertical, and/or as a linear pair.
Example 2:
VERTICAL
1 and 41
23
4
5
Identify each pair of angles as adjacent, vertical, and/or as a linear pair.
Example 3:
ADJACENT
3 and 4 1
23
4
5
Identify each pair of angles as adjacent, vertical, and/or as a linear pair.
Example 4:
ADJACENT,
LINEAR PAIR
1 and 5 1
23
4
5
Find x, y, and z.
Example 5:
51x
yz
129, 51, 129
Find x.
Example 6:
X = 8
( (5 3x x - 15) = + 1) 5 15 3 1x x 2 15 1x 2 16x
(3x + 1)
L
P AT
O
(5x - 15) (20x - 5)(3x + 1)
L
P AT
O
(5x - 15) (20x - 5)
Find
Example 7:
155
m LAT(3x + 1)
L
P AT
O
(5x - 15) (20x - 5)
Since we have already found the value of x, all we need to do now is to
plug it in for LAT.
20 5 20 8 5x ( )160 5
Two angles are supplementary if the sum of their measures is 180 degrees. Each angle is the supplement of the other.
1 2
20160
These are supplements of each other because their angles add up to 180.
x
Example 1 Find the value of x.
x + = 18020
x = 160
20
x
Example 2 Find the value of x.
65
x + = 18065
x = 115
Example 3 Find the value of x.
(7x 10) 3x
(7x + 10) + 3x = 180 10x + 10 = 180
10x = 170
x = 17
Two angles are complementary if the sum of their measures is 90 degrees. Each angle is the complement of the other.
12
3060
These are complements of each other because their angles add up to be 90.
How can I remember the difference between complementary and supplementary? Hmmm…..
A compliment is
just right.
It’s 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.
Example 4 Find the value of x.
x
15x + = 9015
x = 75
Example 5 Find the value of x.
(4x + 3)
(x - 8)
(4x + 3) + (x - 8) = 90
x = 19
5x - 5 = 905x = 95
12
3
5
Are angles 1 and 2 a linear pair?
Are angles 1 and 3 adjacent angles?
Are angles 2 and 3 adjacent angles?
Are angles 3 and 4 a linear pair?
no
no
yes
yes
4
Are angles 4 and 5 supplementary angles?
Are angles 2 and 3 complementary angles?
Are angles 2 and 1 complementary angles?
Are angles 4 and 3 supplementary angles?
no
no
yes
yes
12
3
5
4
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