Angle Pairs
Adjacent Angles
Definition: Two angles that share a common vertex and side but
no common interior points.
Examples:
A
B
36°
22°
1
C
2
D
4
3
Adjacent Angles( a common side )
1 and 2 are adjacent.
1 and ADC are not adjacent.
Non-Adjacent Angles
3 and 4 are not adjacent.
Complementary Angles
Definition: A pair of angles whose sum is 90˚
Examples:
m2 = 50°
A
B
2
Q
A
B
F
2
1
C
Adjacent Angles
( a common side )
m1 = 40°
Q
1
R
G
Non-Adjacent Angles
Supplementary Angles
Definition: A pair of angles whose sum is 180˚
Examples:
B
Adjacent supplementary angles are
also called “Linear Pair.”
2
1
Q
A
C
B
F
m1 = 40°
m2 = 140°
Non-Adjacent Angles
2
A
1
Q
R
G
Examples
< 1 and < 2 are complementary angles. Given m < 1, find m < 2.
a. m1  52
b. m1  19
< 3 and < 4 are supplementary angles. Given m < 3, find m < 4.
a. m3  147
b. m4  38
Examples
< A and < B are complementary angles. Find m < A & m < B.
m  A  5 x  4
m  B  7 x  10
< C and < D are supplementary angles. Find m < C & m < D.
m  C  7 x  3
m  D  x  1
Linear Pair
Definition:Two adjacent angles are a linear pair if their non-common
sides are opposite rays.
The angles in a linear pair are supplementary.
Vertical Angles
Definition: A pair of angles whose sides form opposite rays.
Vertical angles are congruent.
A
1
1 and 3
4
2 and 4
D
B
Q
2
3
C
Vertical angles are non-adjacent angles formed by intersecting lines.
Examples
What are the linear pairs?
What are the vertical angles?
Examples
<1&<3
neither
<2&<3
neither
<4&<5
Linear pair
<8&<5
Vertical angles
<6&<7
Linear pair
<4&<9
Vertical angles
< 1 & < 2 & < 3 neither
Example: If m4 = 67º, find the measures of all other angles.
Step 1: Mark the figure with given info.
Step 2: Write an equation.
m3  m4  180
m3  67 180
67º
3
4
2
1
m3 180  67  113
Because 4 and 2 arevertical angles, they are equal. m4  m2  67
Because 3 and 1 are vertical angles, they are equal. m3  m1  117
Example: If m1 = 23 º and m2 = 32 º, find the
measures of all other angles.
Answers:
m4  23 (1 & 4 are vertical angles.)
m5  32 (2 & 5 are vertical angles.)
m1  m2  m3  180
2
23  32  m3  180
m3  180  55  125
m3  m6  125
3 & 6 are vertical angles.
1
3
6
4
5
Example: If m  1 = 44º, m  7 = 77º
find the measures of all other angles.
Answers: m3  90
m1  m4  44
m4  m5  90
44  m5  90
m5  46
m6  m7  90
m6  65  90
m6  25
4
5
6
3
2
1
7