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" (with an "i") 
Complementary vs Supplementary
A related idea is Complementary Angles, they add up to 90°
How to 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)
You could also think "Supplement" (like a Vitamin Supplement) is something extra, so it it bigger.