Angle Relationships&
Parallel LinesPre-Algebra
Adjacent angles are “side by side” and share a common ray.
45º15º
These are examples of adjacent angles.
55º
35º
50º130º
80º 45º
85º20º
These angles are NOT adjacent.
45º55º
50º100º
35º
35º
Complementary Anglessum to 90°
40°
50°
Complementary angles add up to 90º.
60º
30º40º
50º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
Supplementary Anglessum to 180°
30° 150°
Supplementary angles add up to 180º.
60º120º
40º
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.l||m
120°
l
m
120°
120°
120°
Note the 4 angles that measure 120°.
nLine n is a transversal.
Lines l and m are parallel.l||m
60°
l
m
60°
60°
60°
Note the 4 angles that measure 60°.
nLine n is a transversal.
Lines l and m are parallel.l||m
60°
l
m
60°
60°
60°
There are many pairs of angles that are supplementary.
There are 4 pairs of angles that are vertical.
120°
120°
120°
120°
nLine n is a transversal.
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.
3x°
2x°
3) Solve for x.
3x°
2x°
3x° + 2x° = 90°
5x = 90
x =18
4) Solve for x.
2x + 5
x + 25
4) Solve for x.
2x + 5
x + 25
(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.
4x 5x
7) Solve for x.
4x 5x
4x + 5x = 180
9x = 180
x = 20
8) Solve for x.
2x + 10 3x + 20
8) Solve for x.
2x + 10 3x + 20
(2x + 10) + (3x + 20) = 180
5x + 30 = 180
5x = 150
x = 30
9) Lines l and m are parallel.l||m
Find the missing angles.
42°
l
m
b°
d°
f°
a °
c°
e°
g°
9) Lines l and m are parallel.l||m
Find the missing angles.
42°
l
m
42°
42°
42°
138°
138°
138°
138°
10) Lines l and m are parallel.l||m
Find the missing angles.
81°
l
m
b°
d°
f°
a °
c°
e°
g°
10) Lines l and m are parallel.l||m
Find the missing angles.
81°
l
m
81°
81°
81°
99°
99°
99°
99°
11) Find the missing angles.
70 °b°
70 °
d ° 65 °
Hint: The 3 angles in a triangle sum to 180°.
11) Find the missing angles.
70 °40°
70 °
75 ° 65 °
Hint: The 3 angles in a triangle sum to 180°.
12) Find the missing angles.
45 °b°
50 °
d ° 75 °
Hint: The 3 angles in a triangle sum to 180°.
12) Find the missing angles.
45 °85°
50 °
20° 75 °
Hint: The 3 angles in a triangle sum to 180°.
In the figure a || b.
13. Name the angles congruent to 3.
14. Name all the angles supplementary to 6.
15. If m1 = 105° what is m3?
16. If m5 = 120° what is m2?
1, 5, 7
1, 3, 5, 7
105°
60°
The End
