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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 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

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Page 1: 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 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

Page 2: 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

Page 3: 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

j

im

k h f

e

g

Please Identify in your notes all LINEAR PAIRS

Page 4: 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

j

im

k h f

e

g

SOME POSSIBLE ANSWERS

Page 5: 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

j

im

kh f

e

g

MORE POSSIBLE ANSWERS

Page 6: 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

1 2

1. Determine whether each statement is true or false.

pair.linear a form 2 and 1

Page 7: 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

4 5

2.

pair.linear a form 5 and 4

Page 8: 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

63

3.

angles.adjacent are 3 and 6

Page 9: 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

87

4.

angles.adjacent are 8 and 7

C

A T

Page 10: 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

87

5.

angles.adjacent are 7 and CAT

C

A T

Page 11: 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 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.

Page 12: 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

a b

cd

j

im

k

h f

e

g

Identify all pairs of VERTICAL ANGLES

Page 13: 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

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?

Page 14: 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

1

23

4

5

Identify each pair of angles as adjacent, vertical, and/or as a linear pair.

Example 1:

1 and 2

ADJACENT

Page 15: 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

Identify each pair of angles as adjacent, vertical, and/or as a linear pair.

Example 2:

VERTICAL

1 and 41

23

4

5

Page 16: 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

Identify each pair of angles as adjacent, vertical, and/or as a linear pair.

Example 3:

ADJACENT

3 and 4 1

23

4

5

Page 17: 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

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

Page 18: 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

Find x, y, and z.

Example 5:

51x

yz

129, 51, 129

Page 19: 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

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)

Page 20: 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

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

Page 21: 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 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.

Page 22: 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

x

Example 1 Find the value of x.

x + = 18020

x = 160

20

Page 23: 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

x

Example 2 Find the value of x.

65

x + = 18065

x = 115

Page 24: 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

Example 3 Find the value of x.

(7x 10) 3x

(7x + 10) + 3x = 180 10x + 10 = 180

10x = 170

x = 17

Page 25: 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 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.

Page 26: 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

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.

Page 27: 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

Example 4 Find the value of x.

x

15x + = 9015

x = 75

Page 28: 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

Example 5 Find the value of x.

(4x + 3)

(x - 8)

(4x + 3) + (x - 8) = 90

x = 19

5x - 5 = 905x = 95

Page 29: 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

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

Page 30: 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

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