The geometric figures that are formed by two rays, which share origin
(vertex), are called angles. According to
the supplementary adjective,
on the other hand, refers to that which supplements or complements something.
From these ideas, it is easy to understand what supplementary angles are. These
are those angles that, when added together, result in two right angles. Since
each right angle measures 90º, the sum of the
supplementary angles is equal to 180º (that is, to a flat
In this way, based on all the above, we would come across the fact that the
supplementary angle of 135º would be one of 45º or that the supplementary angle
of 179º is one of 1º.
It is important not to confuse the supplementary angles (which together give 180º)
with the complementary angles (which add up to 90º). While
the supplementary angles are equivalent to two right angles, the complementary
angles are equivalent to a right angle.
In addition to what we have stated so far, it is interesting that we are
aware that in everyday life we find many examples of supplementary
angles. Specifically, these can be found in what are structures of all kinds,
but more exactly in those that are considered to have to support a lot of
What examples do we have around us in this regard? Well, from the arch
bridges that we can see in numerous towns and cities to the tents that are
raised to host an outdoor wedding, also passing through what may be the beam
that exists in a house or premises and that is presented perpendicularly to what
is the ground.
In all these structures we can clearly appreciate what supplementary angles
But not only that, in our day to day, we also have examples of complementary
angles. Specifically, perhaps the clearest example and the one that allows us to
understand more and better what those are like is found in the hands of any
Supplementary angles can be obtained by appealing to arithmetic. Suppose we
intend to find out the supplementary angle b of an angle
a. For this, we must subtract the angle a from 180º and
the result will be angle b, its
For example: if the angle a measures 125º,
when we subtract 125º from 180º we will reach
a result of 55º. We can verify that these are supplementary
angles by adding 125º (angle a) and 55º
b), the result of which is equal to 180º (a flat
angle or two right angles).
Supplementary angles can also be classified in other ways. If these angles
share origin and one side, and their other two sides are opposite rays, they
are adjacent angles. In addition, when having a side and the
vertex in common, they are consecutive or contiguous angles.
In addition to all the above, we must emphasize that supplementary angles
become key pieces within different disciplines, but, above all, in mathematics
and also in architecture.