Supplementary Angles
Two Angles are Supplementary when they add up to 180 degrees.
These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:
Notice that together they make a straight angle.
But the angles don't have to be together.
These two are supplementary because
60° + 120° = 180°
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When the two angles add to 180°, we say they "Supplement" each other. Supplement comes from Latin supplere, to complete or "supply" what is needed. 

Spelling: be careful, it is not "Supplimentary Angle" 
Complementary vs Supplementary
A related idea is Complementary Angles, they add up to 90°
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