Angle Relationships

1
Angle RelationshipsParallel Lines
2
Objectives

• To identify parallel lines
• To use symbols to describe pairs of lines
• To identify exterior, interior, corresponding,
  alternate interior and supplementary angles
• To use a protractor to measure and classify angles

3
Vocabulary

• Parallel lines Lines in the same plane that
  never meet.
• Coplanar Lines or points in the same plane.
• Skew Lines Lines in space that are not coplanar
  and never meet.
• Transversal A line that crosses parallel lines.
• Exterior Angle Angle outside the parallel
  lines.
• Interior Angle Angle inside the parallel lines.
• - symbol for parallel lines
  - not parallel lines

4
Skew Lines
5
Transversal Line
6
Adjacent angles are side by side and share a
common ray.
15º
45º
7
These are examples of adjacent angles.
45º
80º
35º
55º
50º
130º
85º
20º
8
These angles are NOT adjacent.
100º
50º
35º
35º
45º
55º
9
Complementary Anglessum to 90
50
40
10
Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
11
Supplementary Anglessum to 180
150
30
12
Supplementary angles add up to 180º.
40º
60º
120º
140º
Adjacent and Supplementary Angles
Supplementary Anglesbut not Adjacent
13
Vertical Anglesare opposite one
another.Vertical angles are congruent.
100
100
14
Vertical Anglesare opposite one
another.Vertical angles are congruent.
80
80
15
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
16
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
17
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
18
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.
19
Practice Time!
20
1) Find the missing angle.
?
36
21
1) Find the missing angle.
?
36
90 36 54
22
2) Find the missing angle.
?
64
23
2) Find the missing angle.
?
64
90 64 26
24
3) Solve for x.
2x
3x
25
3) Solve for x.
2x
3x
3x 2x 90 5x 90 x 18
26
4) Solve for x.
x 25
2x 5
27
4) Solve for x.
x 25
2x 5
(2x 5) (x 25) 90 3x 30 90 3x 60 x
20
28
5) Find the missing angle.
168
?
29
5) Find the missing angle.
168
?
180 168 12
30
6) Find the missing angle.
?
58
31
6) Find the missing angle.
?
58
180 58 122
32
7) Solve for x.
5x
4x
33
7) Solve for x.
5x
4x
4x 5x 180 9x 180 x 20
34
8) Solve for x.
3x 20
2x 10
35
8) Solve for x.
3x 20
2x 10
(2x 10) (3x 20) 180 5x 30 180 5x
150 x 30
36
9) Lines l and m are parallel.lmFind the
missing angles.
42
a
c
b
l
d
e
g
m
f
37
9) Lines l and m are parallel.lmFind the
missing angles.
42
138
138
42
l
42
138
138
m
42
38
10) Lines l and m are parallel.lmFind the
missing angles.
81
a
c
b
l
d
e
g
m
f
39
10) Lines l and m are parallel.lmFind the
missing angles.
81
99
99
81
l
81
99
99
m
81
40
11) Find the missing angles.
70
70
b
Hint The 3 angles in a triangle sum to 180.
d
65
41
11) Find the missing angles.
70
70
40
Hint The 3 angles in a triangle sum to 180.
75
65
42
12) Find the missing angles.
45
50
b
Hint The 3 angles in a triangle sum to 180.
d
75
43
12) Find the missing angles.
45
50
85
Hint The 3 angles in a triangle sum to 180.
20
75
44
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
45
The End