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Complementary Angles


Note the angles AÔB and BÔC in the figure below:

Verify that:

m (AÔB) + m (BÔC) = 90º

In this case, we say that the angles AÔB and BÔC are complementary. Like this:

Two angles are complementary when the sum of your measurements is 90º.

Example:

The angles measuring 42º and 48º are complementary, since 42º + 48º = 90º.

We say that the angle of 42º is the complement of the angle of 48º, and vice versa.

To calculate the angle complement measure, we must determine the difference between 90 ° and the given acute angle measurement.

Angle measurement Complement
x 90th - x

Example:

  • What is the measure of the complement of an angle of 75º?

Solution

Complement measurement = 90º - angle measurement

Complement measurement = 90º - 75º

Complement measurement = 15º

Therefore, the angle complement measure of 75º is 15º.

Note:

The angles XÔY and YÔZ of the adjacent figure, besides being complementary, are also adjacent. We say these angles are complementary adjoins.

Next: Supplementary Angles