An angle is formed by two rays that share the same vertex as
origin. There are numerous types of angles that differ from each other according
to their characteristics: one of the most common ways of distinguishing them is
taking into account their width.
A flat angle, in this frame, is one that measures 180
°. These are one greater than the null angle (measuring
0 °), the acute angle (greater than 0 ° but less than 90 °),
the right angle (90 °), and the obtuse angle (measuring
more than 90 ° and less than 180 °). Instead, the flat angle is less than the perigonal
angle  also called the full angle  which has an
amplitude of 360 °.
Taking these data into account, we can affirm that a flat angle is equivalent
to two right angles (90 ° + 90 ° = 180 °) and half of a
perigonal angle (360 ° / 2 = 180 °).
If we focus on the construction of a flat angle with vectors, we will notice
that it is the rotation of the vector to completely change its direction. In
other words, when a vector that points in one direction rotates and points to
the opposite direction, it completes a flat angle on its path (it makes a 180 °
turn).
According to
DigoPaul, drawing a flat angle is easy if we use a protractor and a compass. We
only have to make a ray with the protractor, open the compass
from the origin to the end of the ray and then trace a 180 ° turn until we reach
the opposite side. The amplitude of the 180 ° angle places us before a flat
angle.
One of the complementary concepts to the angle is the bisector,
a ray that crosses the vertex of an angle and results in two halves, that is,
two identical parts. It is the locus (the set of points at which certain
properties or conditions are noticed) of the plane that is at the same
distance from each of the two rays that form the angle; in other words, each
point of the bisector is equal distance from both rays.
In the case of flat angles, the bisector is easier to trace than in most
others: since, with the naked eye, an angle of 180 ° is only a line, just
determine its center point, the vertex of the two rays, and
start drawing from there a line perpendicular to both. As a result of the
bisector we obtain two right angles, that is, 90 °.
Angles are a fundamental part of mathematics, but also of any discipline that
uses graphic elements to recreate physical situations,
regardless of the degree of realism. Whether in cartoon series, computer
animation movies, or video games, although the public may not always be aware of
it, it would not be possible to animate a character walking or the trajectory of
a rock flying through the air without calculating many angles simultaneously.
As mentioned in a previous paragraph, the flat angle can be used to graph the
total change of direction of a vector, and this concept is another of
the fundamentals of the aforementioned fields: a video game character has a vector that
indicates its orientation in space moves through the stage following another
vector, and the same is true for all moving objects.
Although mathematics is not liked by most people, in everyday speech there
are many expressions that have their origin in this
science. Focusing specifically on the concept of a flat angle, it is often said
that a situation or life itself takes a 180 ° turn to refer to a drastic or
complete change, from peace to chaos or vice versa.
