Supplement Theorem

Consider two angles that form a linear pair.

Here, $\angle 1$ and $\angle 2$ form a linear pair since their non-common sides are opposite rays. Moreover, the non-common sides form a straight line, which means that $m\angle ABC=180^{\circ }.$ Using the Angle Addition Postulate, $m\angle ABC$ can be written as the sum of $m\angle 1$ and $m\angle 2.$ The above equation implies that $\angle 1$ and $\angle 2$ are supplementary angles.