Chapter 9 - XYZ Custom Plus

9.1 The Distributive Property and Algebraic Expressions
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Example 11
Find x in each of the following diagrams.
a. b.
x
30°
x
45°
Supplementary angles
11. Find x in each of the following
diagrams.
a.
x
45°
Solution
Complementary angles
We use subtraction to find each angle.
a. Because the two angles are complementary, we can find x by
subtracting 30° from 90°:
x 5 90° 2 30° 5 60°
Complementary angles
b.
x
60°
We say 30° and 60° are complementary angles. The complement
of 30° is 60°.
Supplementary angles
b. The two angles in the diagram are supplementary. To find x, we
subtract 45° from 180°:
x 5 180° 2 45° 5 135°
We say 45° and 135° are supplementary angles. The supplement
of 45° is 135°.
Using
Protractors
Technology
When we think of technology, we think of computers and calculators. However,
some simpler devices are also in the category of technology, because
they help us do things that would be difficult to do without them. The protractor
below can be used to draw and measure angles. In the diagram below,
the protractor is being used to measure an angle of 120°. It can also be used
to draw angles of any size.
140
40
130
50
60
120
110
70
80
100
90
90
100
80
110
70
120
60
130
50
140
40
150
30
160
20
120°
150
30
160
20
170
10
170
10
0
180
180
0
0 12345678910 11
If you have a protractor, use it to draw the following angles: 30°, 45°, 60°,
120°, 135°, and 150°. Then imagine how you would draw these angles without
a protractor.
Answer
11. a. 45° b. 120°