Basic Mathematics for College Students

714 Chapter 9 An Introduction to Geometry

3 Identify and name angles.

Angle

An angleis a figure formed by two rays with a common endpoint. The

common endpoint is called the vertex,and the rays are called sides.

The angle shown below can be written as , , , or. The symbol

means angle.

BACCABA  1

Caution! When using three letters to name an angle, be sure the letter name

of the vertex is the middle letter. Furthermore, we can only name an angle

using a single vertex letter when there is no possibility

of confusion. For example, in the figure on the right,

we cannot refer to any of the angles as simply ,

because we would not know if that meant ,

WXZ, or .YXZ

WXY

X

A

B

C

1

Vertex of

the angle

Sides of

the angle

Angle

4 Use a protractor to measure angles.

One unit of measurement of an angle is the degree.The symbol for degree is a small

raised circle, °. An angle measure of 1° (read as “one degree”) means that one side of

an angle is rotated of a complete revolution about the vertex from the other side

of the angle. The measure of , shown below, is 1°. We can write this in symbols

as .m(ABC)1°

ABC

3601

X

Z

Y

W

B

C

A

1 °

This side of the angle is rotated of a complete

revolution from the other side of the angle.

–––^1

360

The following figures show the measures of several other angles. An angle

measure of 90° is equivalent to of a complete revolution. An angle measure of

180° is equivalent to of a complete revolution, and an angle measure of 270°

is equivalent to of a complete revolution.

m(FED)90° m(IHG)180° m(JKL)270°

270360 ^34

180360 ^12

36090 ^14

90 °

D

180 °

E

F G H I

270 °

K

L

J