Complementary and Supplementary Angles

Complementary angles: two angles whose sum is 90º

Supplementary angles: two angles whose sum is 180º

Angles are measured in degrees, minutes, and seconds where 1º = 60’ and 1’ = 60”. For our purposes we will consider angles of degrees or degrees and minutes, and decimal forms, of course.

Consider: What is the complement and supplement of 15º 13’ ?

This calculation is very much like the regrouping process we use in subtraction.

To find the complement of the angle, subtract the angle from 90º. However, you can’t subtract 13’ from 0’.

90º = 89º 60’

- 15º 13’

74º 47’

To find the supplement, 1) subtract from 180º or 2) add 90º (Why does #2 work?)

Suppose you want the two complements that have a ratio of 4:2.

First, realize these angles sum to 90º. Also, in a ratio we know that each angle is made up of equal parts. So, one angle has 4 equal parts or 4x, where x stands for the equal part, and the other angle has 2 equal parts, or 2x. What does our equation become?

4x + 2x = 90º

Solving: 6x = 90º

X = 15º

The angles are 4(15º) = 60º and 2(15º) = 30º.