From Latin: complementum - "that which fills up or completes"

Definition: Two angles that add up to 90°

Try this Drag an orange dot. The two angles will change so that they always add to 90°

In the figure above, the two angles ∠PQR and
∠JKL are complementary because they always add to 90°
Often the two angles are
adjacent, in which case they form a
right angle.

In a
right triangle, the two smaller angles are always complementary.
(Why? - one angle is 90° and all three add up to 180°.
Therefore the two smaller ones must add to 90° and so are complementary by definition).
See the page on right triangles
and convince yourself that this is true.

Sometimes it's hard to remember which is which between supplementary (adds to 180°) and complementary (adds to 90°). Here are two memory aids:

The phrase "it's right to give compliments" A right angle is 90 degrees and, yes, 'compliment' and 'complement' are not the same word, but it's a way to remember which is which.

Put a vertical line on the right of the letter 'c' in 'complementary' to make into a '9'. Complementary angles add to 90.