All supplementary angles do not form a linear pair. The opposite angles of any quadrilateral inscribed in a circle (a cyclic quadrilateral) are supplementary but they are not a linear pair. However, all linear pair are supplementary.
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No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.
Yes.
All supplementary angles would be linear pairs IF they were adjacent. But they could be far apart.
If the lines are perpindicular then each pair of vertical angles are supplementary
yes