adjacent angles

A angle is a geometric figure which is formed with two rays that share the same vertex as an origin. Adjacent, for its part, is an adjective that qualifies what is located next to something.

The adjacent angles They are that share a side and vertex, while the other two sides turn out opposite rays. This definition allows us to infer that the 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 gives as a result 180 °; that is, a flat angle).

It is important to note that not all sources in this topic honor the requirement that both angles add up to a total of 180 °; that is, in many texts of geometry the concept of adjacent angles is defined as any pair that have a side and 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 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 equal.

The cosine It is a concept belonging to trigonometry, and refers to the ratio between the adjacent leg of an acute angle that forms part of a right triangle and its hypotenuse; In other words, we can say that the cosine of the angle α equals 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 a function of the angle, as indicated by the Thales theorem.

On the other hand is the breast, a function of trigonometry that consists of dividing the leg opposite an angle given by its hypotenuse.

If an angle of 44th is located next to an angle of 136 °, with which it shares a side and the vertex, we can say that they are adjacent angles (44 ° + 136 ° = 180 °). This qualification affects both angles, without preventing the development of other classifications. The angle of 44th, in addition to being adjacent to the other, is a acute angle. The angle of 136 °, for its part, 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 rays. If we add both adjacent right angles, the result will be a straight angle (180 °).

As with many other classifications in the field of math, 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 turn 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 present. expressly, but many times we start from just one and we 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.