Any two angles are called Supplementary angles when they add up to 180°. When two angles add to 180°, we say that the angles are “Supplement” to each other. In the pair of supplementary angles if one angle is x°, then its supplement is an angle of (180 - x)° .
Supplementary Angles
From the above figures, we have $\angle$ABD and $\angle$DBC are supplementary because 55°+125°=180°. $\angle$EFG and $\angle$HIK are supplementary because 74°+106°=180°. Also, $\angle$ABD and $\angle$DBC together form straight angle $\angle$ABC. Thus, if two angles are together and are supplement to each other then they have a common vertex and share one side. The other two non-shared sides of the angles form a straight line and have a straight angle. Such kind of angles are called as linear pair. The angles need not be together, but together they add up to 180°. For example, in geometrical figures, the adjacent angles of a rectangle are supplementary, and also the opposite angles of a cyclic quadrilateral are supplementary.

Two angles are supplementary, only when one will be an acute angle and the other will be an obtuse angle or both of them will be right angles.

Supplementary angles are seen in real life in many places. Few examples are shown here.

Supplementary Angles in Real Life

In the figure (i) we notice that the two streets meet at angle of A° and B° at the corners. These two angles sum to 180°. So, these kinds of intersections are examples of supplementary angles.

In the figure (ii) we see a tree which has two branches. We can see supplementary angles U° and D° which are the angle of a branch on a tree from the ground and the angle of that same branch from the sky. These angles add up to 180°, thus forming supplementary angles.

Consecutive angles of a four cornered room, consecutive angles of a four cornered window, consecutive angles of a piece of A4 sheet all are supplement angles.