you discovered that if a pair of angles is a linear pair, then the angles are supplementary. does that mean that all supplementary angles form a linear pair of angles? is the converse true?
The two questions are basically asking the same thing, since the 1st quest is the converse of the original statement.
No, supplementary angles don’t have to be adjacent, they just have to add to 180 degrees. Just show two angles that are completely separated from each other whose angles add to 180 (the simplest case would be two right angles). They aren’t a linear pair since their sides don’t form a line.