Angle RelationshipsParallel Lines

Pre-Algebra

Adjacent angles are side by side and share a

common ray.

15º

45º

These are examples of adjacent angles.

45º

80º

35º

55º

50º

130º

85º

20º

These angles are NOT adjacent.

100º

50º

35º

35º

45º

55º

Complementary Anglessum to 90

50

40

Complementary angles add up to 90º.

30º

40º

50º

60º

Adjacent and Complementary Angles

Complementary Anglesbut not Adjacent

Supplementary Anglessum to 180

150

30

Supplementary angles add up to 180º.

40º

60º

120º

140º

Adjacent and Supplementary Angles

Supplementary Anglesbut not Adjacent

Vertical Anglesare opposite one

another.Vertical angles are congruent.

100

100

Vertical Anglesare opposite one

another.Vertical angles are congruent.

80

80

Lines l and m are parallel.lm

Note the 4 angles that measure 120.

120

120

l

120

m

120

Line n is a transversal.

n

Lines l and m are parallel.lm

Note the 4 angles that measure 60.

60

60

l

60

m

60

Line n is a transversal.

n

Lines l and m are parallel.lm

There are 4 pairs of angles that are vertical.

There are many pairs of angles that are

supplementary.

60

120

120

60

l

60

120

120

m

60

Line n is a transversal.

n

If two lines are intersected by a transversal and

any of the angle pairs shown below are congruent,

then the lines are parallel. This fact is used in

the construction of parallel lines.

Practice Time!

1) Find the missing angle.

?

36

1) Find the missing angle.

?

36

90 36 54

2) Find the missing angle.

?

64

2) Find the missing angle.

?

64

90 64 26

3) Solve for x.

2x

3x

3) Solve for x.

2x

3x

3x 2x 90 5x 90 x 18

4) Solve for x.

x 25

2x 5

4) Solve for x.

x 25

2x 5

(2x 5) (x 25) 90 3x 30 90 3x 60 x

20

5) Find the missing angle.

168

?

5) Find the missing angle.

168

?

180 168 12

6) Find the missing angle.

?

58

6) Find the missing angle.

?

58

180 58 122

7) Solve for x.

5x

4x

7) Solve for x.

5x

4x

4x 5x 180 9x 180 x 20

8) Solve for x.

3x 20

2x 10

8) Solve for x.

3x 20

2x 10

(2x 10) (3x 20) 180 5x 30 180 5x

150 x 30

9) Lines l and m are parallel.lmFind the

missing angles.

42

a

c

b

l

d

e

g

m

f

9) Lines l and m are parallel.lmFind the

missing angles.

42

138

138

42

l

42

138

138

m

42

10) Lines l and m are parallel.lmFind the

missing angles.

81

a

c

b

l

d

e

g

m

f

10) Lines l and m are parallel.lmFind the

missing angles.

81

99

99

81

l

81

99

99

m

81

11) Find the missing angles.

70

70

b

Hint The 3 angles in a triangle sum to 180.

d

65

11) Find the missing angles.

70

70

40

Hint The 3 angles in a triangle sum to 180.

75

65

12) Find the missing angles.

45

50

b

Hint The 3 angles in a triangle sum to 180.

d

75

12) Find the missing angles.

45

50

85

Hint The 3 angles in a triangle sum to 180.

20

75

In the figure a b.

13. Name the angles congruent to ?3.

?1, ?5, ?7

14. Name all the angles supplementary to ?6.

?1, ?3, ?5, ?7

15. If m?1 105 what is m?3?

105

16. If m?5 120 what is m?2?

60

The End