Angle Relationships

1
Angle RelationshipsParallel Lines
Lesson and Practice
2
Adjacent angles are side by side and share a
common ray.
15º
45º
3
These are examples of adjacent angles.
4
These angles are NOT adjacent.
100º
50º
35º
35º
45º
55º
5
Complementary Angleshave a sum of 90
50
40
6
Complementary angles add up to 90º.
Complementary and Adjacent Angles
Complementary Anglesbut not Adjacent
7
Supplementary Angleshave a sum of 180
30
150
8
Supplementary angles add up to 180º.
Supplementary and Adjacent Angles
Supplementary Anglesbut not Adjacent
9
Vertical Anglesare opposite of one another.
Vertical angles are congruent.
80
100
100
80
10
Vertical Anglesare opposite one
another.Vertical angles are congruent.
60
120
120
60
Do you see why?
11
Lines l and m are parallel.l m
Line n is a transversal.
Note the 4 angles that measure 120.
120
120
l
120
120
m
n
12
Lines l and m are parallel.lm
Line n is a transversal.
Note the 4 angles that measure 60.
60
60
l
60
60
m
n
13
Lines l and m are parallel.l m
Line n is a transversal.
There are 4 pairs of angles that are vertical.
60
120
120
60
l
60
120
120
60
There are many pairs of angles that are
supplementary.
m
n
14
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.
15
Practice Time!
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1) Find the missing angle.
?
36
17
1) Find the missing angle.
?
36
90 36 54
18
2) Find the missing angle.
?
64
19
2) Find the missing angle.
?
64
90 64 26
20
3) Solve for x.
2x
3x
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3) Solve for x.
3x 2x 90 5x 90 x 18
2x
3x
22
4) Solve for x.
x 25
2x 5
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4) Solve for x.
x 25
2x 5
(2x 5) (x 25) 90 3x 30 90 3x 60 x
20
24
5) Find the missing angle.
168
?
25
5) Find the missing angle.
168
?
180 168 12
26
6) Find the missing angle.
?
58
27
6) Find the missing angle.
?
58
180 58 122
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7) Solve for x.
5x
4x
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7) Solve for x.
4x 5x 180 9x 180 x 20
5x
4x
30
8) Solve for x.
3x 20
2x 10
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8) Solve for x.
(2x 10) (3x 20) 180 5x 30 180 5x
150 x 30
3x 20
2x 10
32
9) Lines l and m are parallel.l mFind the
missing angles.
42
a
c
b
l
d
e
g
f
m
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9) Lines l and m are parallel.lmFind the
missing angles.
42
138
138
42
l
42
138
138
42
m
34
10) Lines l and m are parallel.l mFind the
missing angles.
81
a
c
b
l
d
e
g
f
m
35
10) Lines l and m are parallel.l mFind the
missing angles.
81
99
99
81
l
81
99
99
81
m
36
11) Find the missing angles.
70
70
b
Hint 2
Hint The 3 angles in a triangle sum to 180.
d
65
37
11) Find the missing angles.
70
70
40
Hint The 3 angles in a triangle sum to 180.
75
65
38
12) Find the missing angles.
45
50
b
Hint The 3 angles in a triangle sum to 180.
d
75
39
12) Find the missing angles.
45
50
85
Hint The 3 angles in a triangle sum to 180.
20
75
40
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
41
The End