Lesson 4 to 6 in Mathematics Grade 7.ppt

Angle Relationships
&
Parallel Lines
Pre-Algebra

Adjacent angles are “side by
side” and share a common ray.
45º
15º

These are examples
of adjacent angles.
55º
35º
50º
130º
80º 45º
85º
20º

These angles are NOT adjacent.
45º
55º
50º
100º
35º
35º

Complementary Angles
sum to 90°
40°
50°

Solve for x.
3x°
2x°
3x° + 2x° = 90°
5x = 90
x =18

Complementary angles add up to 90º.
40º
50º
Adjacent and
but not Adjacent
60º
30º

Supplementary Angles
sum to 180°
30° 150°

Supplementary angles add up to 180º.
60º
120º
40º
140º
Adjacent and
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
l
m
120°
120°
120°
120°
Note the 4
angles that
measure 120°.
n
Line n is a
transversal.

l||m
l
m
60°
60°
60°
60°
Note the 4
angles that
measure 60°.
n
Line n is a
transversal.

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°
n
Line 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.

1) Find the missing angle.
36°
?°

36°
?°
90 ° – 36 = 54°

64°
?°

64°
?°
90 ° – 64° = 26°

3) Solve for x.
8x°
7x°
7x° + 8x° = 90°
15x = 90
x = 6

4) Solve for x.
2x + 5
x + 25
(2x + 5) + (x + 25) = 90
3x + 30 = 90
3x = 60
x = 20

?°
168°

?° 168°
180° – 168° = 12°

58°
?°

58° ?°
180° – 58° = 122°

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 = 180-30
5x = 150
x = 30
5 5

9) Lines l and m are parallel.
l||m
Find the missing angles.
42°
l
m
b°
d°
f°
a °
c°
e°
g°

l||m
42°
l
m
42°
42°
42°
138°
138°
138°
138°

10) Lines l and m are
parallel.
l||m
81°
l
m
b°
d°
f°
a °
c°
e°
g°

l||m
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°.

70 °
40°
70 °
75 ° 65 °
Hint: The 3
angles in a
triangle sum to
180°.

45 °
b°
50 °
d ° 75 °
Hint: The 3
angles in a
triangle sum to
180°.

45 °
85°
50 °
20° 75 °
Hint: The 3
angles in a
triangle sum to
180°.

In the figure a || b.
14. Name all the angles supplementary to 6.
13. Name the angles congruent to 3.
15. If m1 = 105° what is m3?
16. If m5 = 120° what is m2?
1, 5, 7
1, 3, 5, 7
105°
60°

Lesson 4 to 6 in Mathematics Grade 7.ppt

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