Complementary Angles

Two angles are Complementary when they
(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°

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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:

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