Supplementary Angles

Two angles are called supplementary angles, if the sum of their measures is 180.

supplementary angles

In the above figure for supplementary angles, we can see two angles formed at a common vertex B. They are angle CBD and angle ABD. Also, the sum of the two angles is 1800, which is in fact angle of a straight line. Therefore, angle CBD and angle ABD are supplementary angles. Again, each angle is said to be the supplement of the other. x and 1800 – x are collectively called supplementary angles and x is the supplement of 1800 – x, and the latter of the former too.

Example 1:

Write the supplement of the following angles: 1. 500 2. 800

The supplement of an angle x degrees is 1800 – x. Therefore, supplement of 500 is 1800 – 500 = 1300. And, supplement of 800 is 1800 – 800 = 1000

Example 2:

For what degree measure are two supplementary angles equal? Answer: If x0 is an angle, then its supplement is 1800 – x. Since the two supplementary angles are equal, so x = 180 – x, i.e. 2x = 1800. Therefore x = 900. Supplementary angles need not be adjacent angles

In the above figure, the two angles CBD and ABD are adjacent angles, because they are formed at a common vertex B and a common arm BD of the two angles ABD and CBD.

Recall that two angles are adjacent angles if they are formed at a same vertex and also if they have a common arm {ray BD}. But supplementary angles need not necessarily be adjacent angles. In the following figure, the two angles ABC and DEF are also supplementary angles, in spite of not being adjacent angles.


supplementary angles but not adjacent angles