Basic Mathematics for College Students

We can use a protractorto measure angles. To begin, we place the center of the
protractor at the vertex of the angle, with the edge of the protractor aligned with one
side of the angle, as shown below. The angle measure is found by determining where
the other side of the angle crosses the scale. Be careful to use the appropriate scale,
inner or outer, when reading an angle measure.
If we read the protractor from right to left, using the outer scale, we see that

. If we read the protractor from left to right, using the inner scale, we
can see that m(GBF)30°.

m(ABC)30°

9.1 Basic Geometric Figures; Angles 715

(^10080901008070)
11012060
13050
14040
15030
16020
(^17010)
(^1800)
(^11070)
(^12060)
(^13050)
(^14040)
(^15030)
(^16020)
17010
GA^1800 B
F
E
D
C
When two angles have the same measure, we say that they are congruent.Since
and , we can write
Read the symbol as “is congruent to.”
We classify angles according to their measure.

ABC  GBF

m(ABC)30° m(GBF)30°

Classifying Angles

Acute angles:Angles whose measures are greater than 0° but less than 90°.

Right angles:Angles whose measures are 90°.

Obtuse angles:Angles whose measures are greater than 90° but less than 180°.

Straight angles:Angles whose measures are 180°.

40°

Acute angle

90°

Right angle

130°

Obtuse angle

180°

Straight angle

Measure

Angle in degrees

30°

60°

110°

150°

180°

30°

GBC 150°

GBF

ABG

ABF

ABE

ABD

ABC

The Language of Mathematics A symbol is often used

to label a right angle. For example, in the figure on the right,

the symbol drawn near the vertex of indicates that

m(ABC)90°.

 ABC



A

B

C