Two Angles are Complementary if 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°
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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.
|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.
|Spelling: be careful, it is not "Complimentary Angle" (with an "i") ...
that would be an angle you get for free!
Complementary vs Supplementary
Note: 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" (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.