I am trying to understand the underlying difference between two words 'supplementary' and 'complementary', which are both used to describe angles. Two acute angles are called complementary if their measurements add up to 90 degrees. Two angles are called supplementary when either both are right angles, or one is obtuse and another is acute. In fact both words mean that one angle's measure is added to another to get 90 degrees in case of complementary ones, or 180 degrees in case of supplementary ones. I will appreciate your help on finding the answer about that underlying meaning that makes these two words different.

Thank you!