The difference between two complementary angles is 50 then the smaller angle is

Two angles are Complementary when they
add up to 90 degrees (a Right Angle

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

Notice that together they make a right angle

But the angles don't have to be together.

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

(Drag the points)

images/geom-comp-supp.js?mode=comp

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.

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

Complementary comes from Latin completum meaning "completed" ...
because the right angle is thought of as being a complete angle.

Spelling: 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:

• Complementary add to 90°
• Supplementary add to 180°

You can also think:

• "C" of Complementary is for "Corner" (a Right Angle), and
• "S" of Supplementary is for "Straight" (180° is a straight line)

Or you can think:

• when you are right you get a compliment (sounds like complement)
• "supplement" (like a vitamin supplement) is something extra, so is bigger

5231, 5233, 819, 2109, 820, 2110, 5240, 9063, 3305, 3306