By compliment of an angle do you mean something nice someone said about the angle, such as, "My aren't you a cute angle!" Or do you mean something nice the angle said about someone or something else, e.g. "What a clever Geometer you are!"?
If you actually mean that angle whose measure when added to the original angle forms a sum equal to 90 degrees, then you mean the complement of the angle.
I don't know how to find the angels. For that you need to consult your clergyman or spiritual advisor. On the other hand if you really want to find the angles, then proceed as follows:
Let
Depending on the definition your instructor uses for the term "complementary angle", you either have
If the definition you are required to use defines complementary angles in terms of the sum of two acute angles, then you have no solution because an acute angle is strictly less than 90 degrees. So if one of your angles is zero degrees the complement must be 90 which violates the definition because a 90 degree angle is not acute. On the other hand, if your definition is silent about the nature of the angles to be summed to 90 degrees, then indeed 0 and 90 both fit the definition and the solution is as I have demonstrated. Indeed, in the latter case, you could have a pair of complementary angles where one of them was obtuse or even reflex and the other has a negative measure.
The above discussion was necessitated by the fact that the definition of complementary angles varies amoung the sources of information that I have available. Google "complementary angles definition" and compare several of the results to see what I mean. I can't smell what your instructor told you or the contents of your textbook's discussion on the subject, so you will have do do your own analysis from here.
John
My calculator said it, I believe it, that settles it
