A perigonal angle measures 360º.
An angle , a term from the Latin word angŭlus , is a figure that is formed from the intersection of two planes or lines in space or on a surface. According to their characteristics, angles are classified in different ways.
The angle that measures 360° , equivalent to 2π radians , is called perigonal . The perigonal angle can also be called a complete angle or integer angle .
Creating a perigonal angle
It must be taken into account that, in plane geometry, an angle is developed with two rays that are joined at the vertex (the point at which they intersect). The ray that remains fixed is usually called A , while the ray that moves to form the opening of the angle is called B.
That opening that is created between the rays is the amplitude , measured in degrees. In the case of the perigonal angle, the amplitude is 360° , which is why its sides coincide: both ray A and B are located in the same place, they are drawn superimposed, since B makes a complete turn. Therefore, perigonal angles give rise to a circle .
There are various methods to draw a perigonal angle.
Conformation possibilities
It is important to mention that perigonal angles can be formed from the sum of angles of smaller amplitude. If we add four right angles (which are the angles that measure 90° ), we will obtain a perigonal angle ( 90° + 90° + 90° + 90° = 360° ).
Since straight angles measure 180° , the perigonal angle can also be developed by adding two straight angles: 180° + 180° = 360° . Another possibility is that three 120° obtuse angles are consecutive and make up a perigonal angle (since 120° + 120° + 120° is equal to 360° ).
It should be noted, on the other hand, that perigonal angles are concave angles . This is what the angles whose amplitude ranges from 180° to 360° are called.
Study of perigonal angles
All this knowledge about the combinations to form a perigonal angle is not always used for its creation, but is also used to study existing ones. The perigonal angle can be divided into quadrants , just like any circle; for example, in parts measuring a quarter or an eighth. It is then that we can operate with the resulting angles, and to proceed we must rely on the theory corresponding to each type (straight, flat, obtuse, concave, etc.).
We have, therefore, the resource of decomposing a perigonal angle into several angles to carry out different operations with properties that it does not possess. These angles obtained by subdividing a circle may or may not be linked to each other; If they are, then they are called consecutive , and they share one side.
Having said all this, it is clear that the perigonal angle is perhaps very peculiar in that we do not find it in a triangular figure, composed of two semi-straight lines in the shape of a "peak", as happens with all the others, but rather we must assume its presence. in a circle .
The figure in everyday life
In everyday life we can observe perigonal angles in various common objects, since the circumference is one of the most used shapes in the design of commercial products and in many aspects of architecture. The case of the traditional clock is quite particular, because on its surface we can see the seconds and minute hands constantly rotating to form a perigonal angle with the hour hand.
If we think that the hour hand is side A of the angle, that is, the ray that remains fixed, then any of the other two can be side B, which rotates until it makes a complete turn and returns to its position superimposed on the angle. the first.
Bicycle wheels are also circumferences that show quite clearly that they are made up of several angles, thanks to the presence of steel spokes.