Two angles are called supplementary angles, if the sum of their measures is 180^{0}.

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 180^{0}, 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 180^{0} – x are collectively called supplementary angles and x is the supplement of 180^{0} – x, and the latter of the former too.

**Example 1: **

**Write the supplement of the following angles: **

**1. 50 ^{0} 2. 80^{0}**

The supplement of an angle x degrees is 180^{0} – x.

Therefore, supplement of 50^{0} is 180^{0} – 50^{0} = 130^{0}

And, supplement of 80^{0} is 180^{0} – 80^{0} = 100^{0}

**Example 2: **

**For what degree measure are two supplementary angles equal?**

**Answer: **

If x^{0} is an angle, then its supplement is 180^{0} – x.

Since the two supplementary angles are equal, so

x = 180 – x, i.e.

2x = 180^{0}

Therefore x = 90^{0}

**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.