In geometry, complementary angles are angles whose measures sum to 90°. If the two complementary angles are adjacent (i.e. have a common vertex and share just one side) their non-shared sides form a right angle.
In Euclidean geometry, the two acute angles in a right triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees.
The adjective complementary is from Latin complementum, associated with the verb complere, "to fill up". An acute angle is "filled up" by its complement to form a right angle.
Read more about Complementary Angles: Trigonometric Ratios