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.
According to DigoPaul, 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 called full).
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.