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 give it its shape. 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 “crooked”. Later it transcended into Latin in the form of “angulus” and with the meaning of “angle”.
-Complementary, on the other hand, has 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 “-ment”, which can be defined as “medium”, and, finally, the suffix “-ary”. The latter is used to indicate “relative to”.

The concept of complementary angles leads us to focus on the two terms that make up the expression. The angles They are geometric figures that are formed with two rays that have a common origin (vertex). Complementary, for its part, is an adjective that refers to that which complements something. Complementary angles, in this frame, 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 up to 90º.
In addition, we can also indicate that the diagonal of any rectangle is also responsible for configuring complementary angles.

It is possible to use arithmetic to obtain complementary angles. The theory indicates that, to know what is the complementary angle of a angle a, its amplitude must be subtracted from 90º. Thus its complementary angle is obtained, which we could call angle b.

If he angle a measure 30th, 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 (30th) and b (60º), we will notice that the Outcome it is 90º, confirming then that they are complementary angles.

It should be noted that complementary angles can also be in a row or contiguous (when they have the vertex and a common side). 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, the so-called supplementary angles always also arise. The latter are the ones that are characterized because they add up to 180º. Thus, for example, at an angle of 150º we have to state that its supplementary would be the one with 30º and what is a 135º angle, its supplementary would be the one that measures 45º.