In order to know the meaning of the term complementary angles, the first thing to do is discover the etymological origin of the two words that shape it. In this sense, this is what we can expose:
-Angle is a word of Greek origin, since it derives from “ankulos”, which can be translated as “twisted”. Then it transcended into Latin in the form of “angulus” and with the meaning of “angle”.
-Complementary, on the other hand, has a Latin origin. It is the result of the sum of several clearly differentiated parts: the prefix “com-“, which means “union”; the verb “plere”, which is synonymous with “fill”; the element “-mento”, which can be defined as “medium”, and, finally, the suffix “-ario”. The latter is used to indicate “relative to”.
According to DigoPaul, the concept of complementary angles leads us to focus on the two terms that make up the expression. The angles are geometric shapes that are formed by two rays having an origin (vertex) in common. Complementary, meanwhile, is an adjective that refers to what complements something.
Complementary angles, in this framework, are angles that complement each other to form a right angle. In other words: the sum of two complementary angles results in an angle of 90º.
In this way, we can determine, therefore, that in a right triangle we find complementary angles. Yes, the acute angles will be, since one will measure 68º and the other 22º. That is, they will add 90º.
In addition, we can also indicate that the diagonal of any rectangle is also responsible for configuring complementary angles.
It is possible to appeal to arithmetic to obtain complementary angles. The theory indicates that, to know what is the complementary angle of an angle a, you must subtract its amplitude at 90º. Thus, its complementary angle is obtained, which we could call angle b.
If the angle a measures 30º, therefore, we must perform the following calculation: 90º – 30º. In this way we will obtain the angle b (60º). If we add the angles a (30º) and b (60º), we will notice that the result is 90º, thus confirming that these are complementary angles.
It should be noted that the complementary angles can also be consecutive or contiguous (when they have the vertex and one side in common). In this case, the uncommon sides of these angles give rise to a right angle.
If the two complementary angles have an amplitude of 45º, they are also congruent since they measure the same. Another classification of these angles would place them in the group of acute angles (they measure more than 0º and less than 90º).
We cannot ignore that when we speak of complementary angles, there are always so-called supplementary angles. The latter are the ones characterized by adding 180º. Thus, for example, at an angle of 150 º we have to expose that its supplementary would be the one with 30 º and at what is one of 135 º its supplementary would be the one that measures 45 º.