Geometric figures are formed from two half lines. These share an origin, which is called the vertex, together creating what is known as angles. From there we can derive the first part of the concept supplementary angles.
The supplementary adjective, for its part, refers to that which is in charge of complementing or supplying something. With this in mind you can better understand what supplementary angles are.
As a definition we can indicate the following: Supplementary angles are those that, when added to each other, result in two right angles. Since each right angle measures ninety degrees, the sum of the supplementary angles reaches 180º, so it is a straight angle.
In this way, taking all of the above into account, you will be able to know that the supplementary of an angle of 130º is one of 50º, or that of one of 100º is one of 80º. That is, in total they must add up to the aforementioned 180 degrees.
Difference Between Complementary and Supplementary Angles
- Do not make the mistake of confusing them with the supplementary angles, which are those that add up to 180º, with the so-called complementary angles. The latter add up to 90º. Thus, while supplementary angles are the same as two right angles, complementary angles are equal to one right angle.
- Following the same property and formula, an angle that is less than 180º will correspond to an angle that supplements it according to the following formula: Supplementary angle = 180º – (angle that needs a supplement). In this way: 180º – 160º = 20º.
- The application in practice is technical, since it is used to carry out the calculation of architectural angles and of great importance in the world of construction. It also has other applications that we are going to talk about below.
The applications of supplementary angles in real life
- In real or everyday life, supplementary angles are much more present than we may initially think. Specifically, it is possible to find them in all kinds of constructions, but especially in those that have to deal with a high weight.
- This makes them very present in different areas and places such as bridges and their respective arches that we can find in a large number of places. Also in the tents that are set up to host events or simply the support beam of any home or premises and that is present perpendicular to the surface. In all these cases it is possible to appreciate the existence of supplementary angles.
- However, it is not necessary to go that far to find many other examples of this type of angle. For example, you can see it in the hands of a clock, which constantly creates supplementary angles.
- It must be borne in mind that this type of angles can be obtained through arithmetic. In this way it is possible to know the supplementary angle b of the angle a in a simple way. All you have to do is subtract the angle that corresponds to 180º, resulting in the angle b, which is its supplementary, that is, following the formula that we have already mentioned before.
The importance of supplementary angles
Supplementary angles can also come to be classified in other different ways. For example, in the event that they have one side and also the origin, and their two sides consist of half lines that are opposite, these are called adjacent angles. At the same time, if they have a common side and vertex, they are also called consecutive (or adjacent) angles.
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Adjacent angles
Adjacent angles are those in which the same side and the vertex are compared. Opposite rays are found on the other two sides. This makes it possible to indicate that adjacent angles are also contiguous angles, since they have a common side and the same vertex. Therefore, they are also supplementary angles, because their sum gives a straight angle, that is, a result of 180º.
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Consecutive angles
The aforementioned consecutive angles are those that are formed by the sum of three elements that are differentiated from each other, having a common side and the same vertex, being one next to the other.
The sum of the consecutive angles is equal to the angle formed, so they are the sides that do not have the angles in common. These types of angles are also called contiguous angles, and they are also, at the same time, adjacent angles.
In this way it can be determined and taken into account that the adjacent angles are angles that are consecutive and complementary. However, they can also be supplementary, in those cases in which the vertex and one of its sides are shared.
Likewise, it must be kept in mind that these types of angles are fundamental in different disciplines, mainly in the world of architecture and, of course, in mathematics.