"Complementary" is a mathematical term used to define the amount one must add to something to make it "whole." For instance, the complement of an event A is the set of all outcomes in the sample space that are not included in the actual outcomes of event A.
The term complementary can be used in reference to different aspects of mathematics. With angles, the complement is the addition of two acute angles to equal 90 degrees. In probability, the complement of an event is all outcomes that are not the event itself. For example, when flipping a coin, if the actual event is "heads," then the complement is "tails." In probability mathematics, the combined event and complement make all possible outcomes.