Complementary angles

Complementary means to complete or fit with the other. In Geometry, the complementary angle in the amount by which an angle falls short of a right angle, 90°.

In the context of triangles, you can think of the complementary angle as follows. The angles of a triangle add up to 180°. The right angle takes up 90° and that leaves 90° remaining. Therefore, the size of the unlabelled angle is 90 – 40 = 50°. The complementary angle to the 40° angle is 50° because that angle completes the triangle

The other way to think of the complementary angle is to simply think how short the angle is of 90°. The 40° angle shown is 50° short of a right angle and so the complementary angle to 40° is 50°.