Complementary Angles

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

 

say If 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.
   
spell 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 can you remember which is which? Easy! Think:

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

Or you can think: when you are right you get a compliment (sounds like complement).

Or you could also think: "Supplement" (like a Vitamin Supplement) is something extra, so it it bigger.