1.5 Exploring
Angle Pairs
Adjacent Angles
Two angles that share a common vertex and side but no common interior points.
1 and ADC are not adjacent.
Adjacent Angles( a common side )
Non-Adjacent Angles
22°
36°
21
D
B
C
A
4
3
Definition:
Examples:
1 and 2 are adjacent.
3 and 4 are not adjacent.
Complementary Angles
A pair of angles whose sum is 90˚Definition:
Examples:
Adjacent Angles( a common side )
21
Q
AB
C 1
2
Q
R
AB
F
G
Non-Adjacent Angles
m1 = 40°m2 = 50°
Supplementary Angles
A pair of angles whose sum is 180˚Definition:
Examples:
Adjacent supplementary angles are also called “Linear Pair.”
Non-Adjacent Angles
2 1
A Q
B
C
1
2
A QR
BF
Gm2 = 140°
m1 = 40°
Examples
< 1 and < 2 are complementary angles. Given m < 1, find m < 2.
a. 521m b. 191m
< 3 and < 4 are supplementary angles. Given m < 3, find m < 4.
b. a. 383m 1473m
382m 712m
334m 1424m
Examples
< A and < B are complementary angles. Find m < A & m < B.
107
45
xBm
xAm 5 𝑥+4+7 𝑥−10=9012𝑥−6=90
12𝑥=96𝑥=8
𝑚<𝐴=5 (8 )+4
𝑚<𝐴=40+4
𝑚<𝐴=44
𝑚<𝐵=7 (8 )−10
𝑚<𝐵=56−10
𝑚<𝐵=46
Examples
< C and < D are supplementary angles. Find m < C & m < D.
1
37
xDm
xCm
7 𝑥−3+𝑥−1=1808 𝑥−4=180
8 𝑥=184𝑥=23
𝑚<𝐶=7 (23 )−3
𝑚<𝐴=161−3
𝑚<𝐴=158
𝑚<𝐵=(23 )−1
𝑚<𝐵=23−1
2
Linear Pair
Two adjacent angles are a linear pair if their non-common sides are opposite rays.
Definition:
The angles in a linear pair are supplementary.
Vertical Angles
A pair of angles whose sides form opposite rays.
Definition:
4
3
2
1A
Q
D
B
C
2 and 4
1 and 3
Vertical angles are non-adjacent angles formed by intersecting lines.
Vertical angles are congruent.
Examples
What are the linear pairs?
What are the vertical angles?
<4 and <5
<1 and <5
Examples< 1 & < 3
< 2 & < 3
< 4 & < 5
< 8 & < 5
< 6 & < 7
< 4 & < 9
< 1 & < 2 & < 3
neither
Linear pair
Vertical angles
Linear pair
Vertical angles
neither
neither
Example: If m4 = 67º, find the measures of all other angles.
3 4 180m m
3 67 180m
3 180 67 113m
3 1 , . 3 1 117 Because and are vertical angles they are equal m m
4
3
2
1
67º
Step 1: Mark the figure with given info.
Step 2: Write an equation.
4 2 , . 4 2 67 Because and arevertical angles they are equal m m
Example: If m1 = 23 º and m2 = 32 º, find the measures of all other angles.
4 23 ( 1 & 4 .)
5 32 ( 2 & 5 .)
m are vertical angles
m are vertical angles
1 2 3 180
23 32 3 180
3 180 55 125
3 6 125
3 & 6 .
m m m
m
m
m m
are vertical angles
6 5
4 3 2
1
Answers:
Example: If m 1 = 44º, m 7 = 77º find the measures of all other angles.
3 90m
1 4 44m m
4 5 90
44 5 90
5 46
m m
m
m
6 7 90
6 65 90
6 25
m m
m
m
7
6 5 4
3
2 1
Answers: