No, they are generally not supplementary.

Not necessarily. A linear pair of angles must be supplementary but supplementary angles need not form a linear pair. For example, the opposite angles of a cyclic quadrilateral are supplementary but they are (by definition) not next to one another.

False. Supplementary angles add to 180degrees.

Supplementary angles have a sum of 180 degrees, while complementary angles have a sum of 90 degrees.

It means added to something to improve it. So you could write: the school was building a supplementary building for a swimming pool to go in.