If two angles are supplements to the same or congruent angles then the angles are congruent. The proof is very similar with the exception that the angles add to 90 degrees and the reason is Definition of complementary angles. 2.5 Addition and Subtraction Properties Recognizing when to use addition and subtraction can be easy as long as you look to see whether you are starting with large angles or segments and ending with smaller or the reverse. If congruent segments are added to congruent segments then the resulting segments are congruent. If two pair of adjacent congruent angles are added together then the resulting angles must be congruent.
Subtraction is the reverse process.
If you start with large congruent angles and subtract off smaller congruent angles, what is left will be congruent. If segments or angles are congruent then their multiples are congruent. The key to recognizing these two properties is to make sure that you have two congruent angle or segments to start with. In geometry we use this property when we have a series of congruent segments or angles that we wish to make congruent.