Pre-Algebra Chapter 9

The most common unit of measure for angles
is the degree. A circle can be separated into
360 arcs of the same length. An angle has a
measurement of one degree if its vertex is at
the center of the circle and the sides contain
the endpoints of one of the 360 equal arcs.
You can use a protractor to measure angles.
1 degree (˚)
Example 1
Measure Angles
a. Use a protractor to measure CDE.
Step 1
Place the center point of
the protractor’s base
on vertex D. Align the
straight side with side
DE so that the marker
for 0° is on the ray.
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160
10
170
30
150
40
140
C
50
130
60
120
70
110
80
100
D
90
100
80
110
70
60
120
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130
140
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160
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E
Step 2
Use the scale that begins
with 0° at DE . Read
where the other side of
the angle, DC , crosses
this scale.
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160
30
150
120˚
C
40
140
50
130
60
120
70
110
80
100
90
100
80
110
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120
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140
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20
Reading Math
The measure of angle CDE is 120°.
Using symbols, mCDE 120°.
10
170
D
170
10
E
Angle Measure
Read mCDE 120˚ as
the measure of angle CDE
is 120 degrees.
b. Find the measures of KXN,
MXN, and JXK.
mKXN 135°
XN is at 0° on the right.
K
40
140
50
130
60
120
70
110
80
100
90
100
80
110
70
M
60
120
50
130
140
40
mMXN 70°
XN is at 0° on the right.
mJXK 45°
XJ is at 0° on the left.
J
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160
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30
150
X
150
30
160
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170
10
N
Protractors can also be used to draw an angle of a given measure.
Example 2
Draw Angles
Draw X having a measure of 85°.
Step 1 Draw a ray with endpoint X.
X
Step 2
Step 3
Place the center point of the
protractor on X. Align the
mark labeled 0 with the ray.
Use the scale that begins
with 0. Locate the mark
labeled 85. Then draw the
other side of the angle.
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160
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170
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150
40
140
50
130
60
120
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110
80
100
X
90
100
80
85˚
110
70
60
120
50
130
140
40
150
30
160
20
170
10
448 Chapter 9 Real Numbers and Right Triangles