Complementary Angles

Two angles are Complementary when they
add up to 90 degrees
(a Right Angle right angle).

complementary angles 40 and 50


These two angles (40° and 50°) are Complementary Angles, because they add up to 90°:

Notice that together they make a right angle right angle.



complementary angles 27 and 63

But the angles don't have to be together.

These two are complementary because 27° + 63° = 90°

Play With It ...

(Drag the points)


complementary right angle triangle 22 and 68

Right Angled Triangle

In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle.


sayWhen two angles add to 90°, we say they "Complement" each other.

comes from Latin completum meaning "completed" ...
because the right angle is thought of as being a complete angle.
spellSpelling: be careful, it is not "Complimentary Angle" (with an "i") ...
that would be an angle you get for free!

Complementary vs Supplementary

A related idea is Supplementary Angles - those add up to 180°

How to remember which is which? Well, alphabetically they are:

You can also think:

Or you can think: