It is known as angle to the figure of the geometry that is composed of two rays, which have the same vertex as origin. Convex, on the other hand, it is an adjective that qualifies what is curved outwards.
In other words, a surface Convex is one that, from the observer’s point of view, has 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 of these mirrors is ideal for widening the person’s field of vision, since the outward curve captures images impossible to perceive from the same point by a human eye. Due to its shape, distortion becomes unavoidable, but this does not prevent its usefulness or cause any risk as long as the user knows how to use it properly and understands the «effects»Visuals that it can cause, such as an alteration in the distance of objects (those close to the center seem closer than the others).
The idea of convex angles appears when, in the same plane, there are two rays that share the vertex of origin and are not aligned or coincident. These rays give rise to two angles: one is a convex angle, while the remainder is a concave angle.
The convex angle is the one that has a smaller amplitude, measuring more than 0 ° but less than 180 °. The concave angleOn the other hand, it is the widest, with an amplitude greater than 180 ° and less than 360 °.
If we return to the definition of the adjective convex and we analyze the complementary relationship that exists between convex and concave angles, we can understand that, in some way, the point of view used to study them is on the convex side, just as it should happen in real life when appreciating a mirror with this type of curvature.
In the same way, the concave angle that complements the convex one must be observed in such a way that the rays close towards us, as if they were two arms trying to wrap us around us.
These definitions reveal that the convex angles are less than the plain angles (180 °) and that the perigonal or full angles (360 °). Instead, they are greater than null angles (0 °). Continuing with this analysis of the angles according to their measurement, we can say that 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 concepts holding 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 bit of information. First, let’s start with the concave angle, which must be greater than 180 ° (since in that case we are talking about straight angle), and less than 360 ° (because the convex must measure at least 1 °, and 360 ° angles are called complete).
With respect to the convex angle, it cannot reach 180 ° so as not to become flat, nor exceed that measure, since from the observer’s perspective it would not be possible to distinguish the portion that exceeds 179 ° of the corresponding concave angle.
A polygon whose interior angles are all less than 180 °, on the other hand, is called convex polygon.