Step-by-step explanation:
supplementary angles are two angles that are together 180°.
they don't have to be adjacent, but the fact that the 2 angles can be placed "randomly" in a scenario is rarely used, except maybe for intersection angles of a line with parallel lines.
a linear pair are 2 angles that are truly adjacent (neighbors, touching each other) that are together 180°.
so, our original statement is
if 2 angles are supplementary, then the angles are a linear pair.
that by itself is (as described) not true in all cases. angles can be non-adjacent (and therefore not a linear pair) and still be supplementary.
so the original statement is false.
(a)
the inverse is
if 2 angles are not supplementary, then the angles are not a linear pair.
that is true.
as per the definition, linear pair angles are a true subset of supplementary angles (every linear pair is a pair of supplementary angles, but not every pair of supplementary angles is a linear pair).
so, if they are not a member of the set of supplementary angles, they cannot be a member of a subset either.
(b)
the converse is
if 2 angles are a linear pair, then the angles are supplementary.
that is true.
because linear pair angles are a true subset of supplementary angles. if something is a member of a subset, it is also a member of any superset.
(c)
the contrapositive is
if 2 angles are not a linear pair, then the angles are not supplementary.
that is false.
as described, linear angles are a true subset of supplementary angles. so, an element can be outside a subset but still inside a superset.
like in the original example, 2 angles across intersected parallel lines can be supplementary, but they are not a linear pair.
