Download Angle Relationships ppt.

Angle Relationships
&
Parallel Lines
Pre-Algebra
www.ih.k12.oh.us/MSDunlap/Geometry/Angle%20Relationships.ppt
Adjacent angles are “side by side” and
share a common ray.
15º
45º
These are examples of adjacent angles.
80º
45º
35º
55º
130º
85º
20º
50º
These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º
Complementary Angles
sum to 90°
50°
40°
Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary
Angles
Complementary Angles
but not Adjacent
Supplementary Angles
sum to 180°
30°
150°
Supplementary angles add up to 180º.
40º
120º
60º
Adjacent and Supplementary
Angles
140º
Supplementary Angles
but not Adjacent
Vertical Angles
are opposite one another.
Vertical angles are congruent.
100°
100°
Vertical Angles
are opposite one another.
Vertical angles are congruent.
80°
80°
Lines l and m are parallel.
l||m
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.
l||m
Note the 4
angles that
measure 60°.
60°
60°
l
60°
60°
Line n is a transversal.
n
m
Lines l and m are parallel.
l||m
There are 4 pairs of
angles that are
vertical.
There are many
pairs of angles that
are supplementary.
60°
120°
120°
Line n is a transversal.
60°
l
60°
120°
120°
60°
n
m
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.
?°
180° – 168° = 12°
168°
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
4x + 5x = 180
9x = 180
x = 20
5x
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°
a°
c°
b°
d°
e°
g°
f°
l
m
9) Lines l and m are parallel.
l||m
Find the missing angles.
42°
138°
138°
42°
42°
138°
138°
42°
l
m
10) Lines l and m are parallel.
l||m
Find the missing angles.
81°
a°
c°
b°
d°
e°
g°
f°
l
m
10) Lines l and m are parallel.
l||m
Find the missing angles.
81°
99°
99°
81°
81°
99°
99°
81°
l
m
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
Sources
www.ih.k12.oh.us/MSDunlap/Geometry/Angle%20Relationships.ppt