two angles are adjacent if they share a common vertex and side, but have no common interior points....

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