The sum of the supplementary angles is equivalent to 180º.
Geometric figures that are formed by two rays, which share an origin (vertex), are called angles . The adjective supplementary , for its part, 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, a straight angle ). In this way, based on everything explained above, we would come across the fact that the supplementary of an angle of 135º would be one of 45º or that the supplementary of an angle of 179º is one of 1º.
It is important not to confuse supplementary angles (which add up to 180º ) with complementary angles (which add up to 90º ). While supplementary angles are equivalent to two right angles, complementary angles are equivalent to one right angle.
Examples of supplementary angles
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, we can find these in structures of all types, but more specifically 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 erected 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 the ground is.
In all of these structures we can clearly see what are supplementary angles.
But not only that, in our daily lives, we also have examples of complementary angles. Specifically, perhaps the clearest example and the one that allows us to understand more and better what these are like is found in the hands that any clock has.
Supplementary angles are studied in geometry.
Using arithmetic
Supplementary angles can be obtained by appealing to arithmetic. Suppose we want to find the supplementary angle b of an angle a . For this, we must subtract the angle a from 180º and the result will be the angle b , its supplementary.
For example: if 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 straight angle or two right angles).
Supplementary angles can also be classified in other ways. If these angles share an origin and a side, and their other two sides are opposite rays, they are adjacent angles . Furthermore, since they have a side and a vertex in common, they are consecutive or contiguous angles .
In addition to everything stated above, we have to emphasize that supplementary angles become key pieces within different disciplines, but, above all, in mathematics and also in architecture.