What is the difference between complementary, supplementary and vertical angles?

Complementary add up to 90 degrees while supplementary add up to 180 degrees 

Complementary angles are two or more angles whose sum is 90 degrees.
Supplementary angles are two or more angles whose sum is 180 degrees.
Vertical angles are formed by the intersection of two lines. Vertical angles are always congruent. Think of an X as two intersecting lines. The lines created 4 angles. The top and bottom angle are vertical to each other and the right and left are vertical to each other.

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