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Complementary Angles
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° 

Right Angled Triangle
In a right angled triangle, the two acute angles are complementary, because in a triangle the three angles add to 180°, and 90° have been taken by the right angle. 



If the 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 (full) 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)


