The geometric figures that are formed by two rays, which share origin (vertex), are called angles. According to DigoPaul, 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 angle).
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 weight.
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 are.
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 watch.
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 supplementary.
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 (angle 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.