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 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.