If the sum of the measures of two angles is 90⁰
Then the angles are called complementary angles.
Each of the angles is called the complement of the other angle.
For example, if one angle measures 30⁰, then the measure
of it's complement is (90-30), or 60⁰.
Remember......
Complementary angles are a pair of angles....
If the sum of the measure of 3 or more angles
is 90⁰, that does not make them complementary angles!

Let's look at some examples of problems
involving complementary angles.

Example 1
Tell whether or not the following pairs of angles are complementary:

10⁰ and 80⁰?
Yes!
10 + 80 = 90

55⁰ and 45⁰?
No!
55 + 45 = 100, not 90!

36 1/2⁰ and 53 1/2⁰?
Yes!
36 1/2 + 53 1/2 = 90

Example 2
Two angles are complementary. 
The measure of one of the angles is 24⁰ greater than the
measure of the other angle. 
Find the measure of each of the angles.

Let x = the smaller angle
Let x + 24 = the larger angle
(x) + (x+24) = 90
2x + 24 = 90
2x = 66
x = 33
Therefore x, the smaller angle, measures 33⁰
and x+24, the larger angle measures 57⁰.

Example 3
Find the number of degrees in angle which exceeds
three times it's complement by 22⁰.

Let x = the smaller complementary angle
Let 3x+22 = the larger complementary angle.
(x) + (3x+22) = 90
4x + 22 = 90
4x = 68
x = 17
Therefore the smaller angle, x, is 17⁰,
and the larger angle, 3x+ 22, is 73⁰.

To try some on your own...

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