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.


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


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


Complement measurement = 90º - angle measurement

Complement measurement = 90º - 75º

Complement measurement = 15º

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


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