An angle is a geometric figure that is formed with two rays that share the same vertex as an origin. Adjacent, meanwhile, is an adjective that qualifies what is located next to something.
According to DigoPaul, the adjacent angles are those that share one side and the apex, while the other two sides are opposite rays. 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 on this topic respect the requirement that both angles total 180 °; that is, in many geometry texts the concept of adjacent angles is defined as any pair that have a 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 the adjacent angles is that their cosines have the same value, although inverse signs, that is to say that their absolute value is the same; for example, if we take two adjacent angles, one of 120 ° and the other of 60 °, the cosine of the first is equal to that of the second multiplied by -1. The breasts of these angles, on the other hand, are the same.
The cosine is a concept belonging to trigonometry, and refers to the ratio of the adjacent leg of an acute angle that is part of a triangle and its hypotenuse; In other words, we can say that the cosine of angle α 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 is rather a function of the angle, as indicated by Thales’ Theorem.
On the other hand is the sinus, a function of trigonometry that consists of 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 these are adjacent angles (44 ° + 136 ° = 180 °). This rating affects both angles, without preventing the development of other ratings. The 44 ° angle, in addition to being adjacent to each other, is an acute angle. The angle of 136 °, on the other hand, is adjacent to this acute angle, but in turn it is an obtuse angle.
Two right angles (90 ° each) can also be adjacent angles. The requirement is always the same: they must share a vertex and one side and the other two sides must be opposite rays. 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 resort to a reliable source to study all its known properties, and evaluate its usefulness for our project.
We can say that the two angles necessary to give life to this concept are not always expressly present, but that we often start from one and 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 are born from observation and theorizing, with which they allow us to mold reality to our needs.