Page 647 - Basic College Mathematics with Early Integers

624 C HAPTE R 9 I GEOMETRY

Solution:
a. ∠R is a right angle, denoted by . It measures 90°.
b. ∠S is a straight angle. It measures 180°.
c. ∠T is an acute angle. It measures between 0° and 90°.
d. ∠Q is an obtuse angle. It measures between 90° and 180°.
Work Practice 3

Let’s look at ∠B below, whose measure is 62°.

62
B
There is a shorthand notation for writing the measure of this angle. To write
“The measure of ∠B is 62°,’’ we can write,
5
T T T T
m∠B = 62°.
By the way, note that ∠B is an acute angle because m∠B is between 0° and 90°.

Objective Identifying Complementary
and Supplementary Angles

Two angles that have a sum of 90° are called complementary angles. We say that
each angle is the complement of the other.
∠R and ∠S are complementary angles because

Î
Î
m∠R + m∠S = 60° + 30° = 90°

60
30
R S
Complementary angles
60 30 90
Two angles that have a sum of 180° are called supplementary angles. We say
that each angle is the supplement of the other.
∠M and ∠N are supplementary angles because

Î
Î
m∠M + m∠N = 125° + 55° = 180°

125
55
M N
Supplementary angles
125 55 180

PRACTICE 4 Example 4 Find the complement of a 48° angle.
Find the complement of a 29° Copyright 2012 Pearson Education, Inc.
angle. Solution: Two angles that have a sum of 90° are complementary.This means that
the complement of an angle that measures 48° is an angle that measures
90° - 48° = 42°.
Answer
4. 61° Work Practice 4