Co-interior angles lie between two lines and on the same side of a transversal.
In each diagram the two marked angles are called co-interior angles.
If the two lines are parallel, then co-interior angles add to give 180o and so are supplementary. In the diagram below the angles ∠CGF and ∠AFG are supplementary.
Conversely, if a pair of angles are supplementary, then the lines are parallel. Line segment CD is parallel to line segment AB, because ∠CGF + ∠AFG = 180°.