Basic Mathematics for College Students

of their measures is 90°.Each angle is said to be the complement of the other.In figure (b)
below, and are also complementary angles, because.
Figure (b) illustrates an important fact: Complementary angles need not be adjacent
angles.

X Y m(X)  m(Y)  90°

ABC CBD

9.1 Basic Geometric Figures; Angles 719

30°

60°

A 15°

B

D

(a) (b)

60° + 30° = 90° 15° + 75° = 90°

Complementary angles

C

X

75°

Y

Supplementary angles

102°

(a) (b)

H

78°

G

MPN

O

50° 130°

50° + 130° = 180° 78° + 102° = 180°

In figure (a) below, and are supplementary angles because the
sum of their measures is 180°. Each angle is said to be the supplement of the other.
Supplementary angles need not be adjacent angles. For example, in figure (b) below,
Gand are supplementary angles, H because .m(G)  m(H)  180°

MNO ONP

Caution! The definition of supplementary

angles requires that the sum of two angles be

180°.Three angles of 40°, 60°, and 80° are not

supplementary even though their sum is 180°.^80 °^40 °

60 °

EXAMPLE 5

a. Find the complement of a 35° angle.

b. Find the supplement of a 105° angle.

Strategy We will use the definitions of complementary and supplementary angles
to write equations that mathematically model each situation.

WHY We can then solve each equation to find the unknown angle measure.

Self Check 5

a. Find the complement of a

50° angle.

b. Find the supplement of a

50° angle.

Now TryProblems 77 and 79