Supplementary Angles

régua e esquadro

Two angles are considered supplementary when the sum of their measures is equal to 180º. For example, the angles with 120º and 60º are supplementary, because 120º + 60º = 180º. It is said that the angle of 60° is the supplement of the angle of 120°, and vice versa. To calculate the measure of the supplement of an angle, simply determine the difference between 180° and the measurement of the given angle.

In the following drawing, we can see that `AhatBD + DhatBC` is always equal to 180º.

Created with GeoGebra by Vitor Nunes


Moves the point `D` to obtain different angles measurements. Check that the sum is always 180º.


Bloco de notas

If the two supplementary angles are adjacent (i.e. have a common vertex and share just one side), their non-shared sides form a straight line. Such angles are called a linear pair of angles. However, supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram are supplementary.