What Are Complementary Angles?

Complementary angles add up to $90^\circ$

When two angles' measures add up to $90^\circ$, the angles are called complementary (to each other). Since angles have to measure less than $90^\circ$ to add up to a right angle, only acute angles can be complementary to each other.

In the image above, angles ABC and DEF are complementary. We can tell because they're congruent with angles GHJ and JHI (respectively), and we can tell from the picture that GHJ and JHI add up to make GHI... which is a right angle.