A angle is a geometric figure It is formed with two semi-lines that share the same vertex as a source. Adjacent , meanwhile, is an adjective that qualifies what is located next to something.
The adjacent angles They are that share one side and the vertex , while the other two sides result opposite half-lines . This definition allows us to infer that adjacent angles are also contiguous or consecutive angles (because they have a common side and the same vertex) and supplementary angles (the sum of both results in 180° ; that is, a flat angle ).
It is important to note that not all sources of this topic respect the requirement that both angles total 180 °; that is, in many texts of geometry the concept of adjacent angles is defined as any pair that have one side and the vertex in common, without the need for them to be supplementary. For this reason, before consulting information in this regard, it is necessary to identify the convention to which it responds, to avoid contradictions or lack of consistency.
Other properties of adjacent angles is that their cosines they have the same value , although inverse signs, that is to say that its absolute value is the same; For example, if we take two adjacent angles, one of 120 ° and one of 60 °, the cosine of the first is equal to that of the second multiplied by -1. The breasts of these angles, however, are equal.
He cosine it is a concept belonging to trigonometry, and refers to the ratio between the adjacent leg of an acute angle that is part of a right triangle and its hypotenuse; in other words, we can say that the cosine of the angle α It is equal to the division of its adjacent leg by the value of the hypotenuse. It should be noted that the result does not vary according to the characteristics of the right triangle, but that it is a function of the angle, as indicated by the Thales theorem .
On the other hand is the breast , a function of trigonometry that consists in dividing the opposite leg at an angle given by its hypotenuse.
If an angle of 44° is located next to an angle of 136° , with which it shares a side and the vertex, we can say that it is about adjacent angles (44° + 136° = 180° ). This rating affects both angles, without impeding the development of other classifications. The angle of 44° , in addition to being adjacent to the other, is a acute angle . The angle of 136° , meanwhile, is adjacent to this acute angle, but in turn is a obtuse angle .
Two right angles (from 90° each) can also be adjacent angles. The requirement is always the same: they have to share a vertex and one side and the other two sides must be opposite straight. If we add both adjacent right angles, the result will be a flat angle (180° ).
As with many other classifications in the field of mathematics , the concept of adjacent angles can be applied to many different problems. Once we identify the type of angle we are facing, the next step is to use a reliable source to study all its known properties, and evaluate its usefulness for our project.
We can say that not always the two angles necessary to give life to this concept are present expressly, but many times we start from one and only imagine the other to access these properties , if this opens the doors to new solutions . In other words, we must not forget that these are concepts that arise from observation and theorization, which allow us to adapt reality to our needs.