An angle is known as the figure of the geometry that is made
up of two rays, which have the same vertex as the origin. Convex,
meanwhile, is an adjective that qualifies what is curved outwards.
In other words, a convex surface is one that, from the point
of view of the observer, presents a more prominent curve in the center than on
the sides, that is, its central point is closer to the observer than the
edges. A clear example in which these characteristics are appreciated is the convex
mirror, widely used to improve the visibility of certain specific
areas, generally close to a corner, such as the exit of a parking lot, or even
in cars, on the passenger side.
the convex angle that these mirrors have is ideal for expanding the
person's field of vision, since the outward curve captures images that
cannot be perceived from the same point by a human eye. Due to its shape,
distortion becomes unavoidable, but this does not impede its usefulness or
create any risk as long as the user knows how to use it properly and understands
the visual " effects " it can cause, such as altering the
distance of objects (those close to the center seem closer than the others).
The idea of convex angles appears when, on the same plane,
there are two rays that share the vertex of origin and that are
neither aligned nor coincident. These rays give rise to two angles: one is a
convex angle, while the rest is a concave angle.
The convex angle is the one with the smallest amplitude, measuring
more than 0 ° but less than 180 °. The concave angle,
on the other hand, is the widest, with an amplitude greater than 180 ° and less
than 360 °.
If we return to the definition of the adjective convex and analyze
the complementary relationship that exists between the convex and concave
angles, we can understand that, somehow, the point of view used
to study them is on the convex side, just as it should occur in the real life
when appreciating a mirror with this type of curvature.
Similarly, the concave angle that complements the convex must be observed in
such a way that the rays are closed towards us, as if they were two arms trying
to envelop us.
These definitions reveal that the convex angles are less than the flat
angles (180 °) and that the perigonal or full angles (360
°). Instead, they are greater than the null angles (0
°). Continuing with this analysis of the angles according to their measurement,
we can say that the convex angles can be acute angles (more
than 0 ° and less than 90 °), right angles (90 °) or even obtuse
angles (more than 90 ° and less than 180 °).
In this framework, there are those who simplify the concepts by maintaining
that angles less than 180 ° are convex angles, while angles greater than 180 °
are concave angles.
The limitation of the degrees presented by each of these two types of angles
is easy to understand if we add a little information. First,
let's start with the concave angle, which must be greater than 180 ° (since in
that case we are talking about a flat angle), and less than 360 °
(because the convex must measure at least 1 ° and, anyway, 360 ° angles are
With respect to the convex angle, it cannot reach 180 ° so as not to become
flat, nor exceed that measure, since from the perspective of
the observer it would not be possible to distinguish the portion that exceeds
179 ° from the corresponding concave angle.
A polygon whose interior angles are all less than 180 °, on the other hand,
is called a convex polygon.