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
socalled 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.
