Convex angle

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The convex angle is one that measures less than 180º or π radians, that is, it is less than a straight angle, but greater than a null angle.

The convex angle is one of the categories of angles based on their measure.

It should be remembered that an angle is an arc that is formed by the intersection of two lines, rays, or segments.

Another concept to take into account is that of convexity, which is that characteristic by which a surface has a greater subsidence at the edges than in the central part. Take, for example, the surface of a sphere or a crystal ball.

The opposite of a convex angle is a concave angle, which is one that measures between 180º and 360º.

It is worth noting that the crossing of two rays (which do not form a flat angle) form a convex angle and another concave, the sum of both being equal to a complete angle (360º). We can see this in the lower image where the convex angle measures 71.3º and the concave, 288.7º.

Another fact to take into account is that those polygons where all their interior angles measure less than 180º are called convex polygons.

Types of convex angles

There can be three types of convex angles:

  • Acute angle: It is that angle less than 90º.
  • Obtuse angle: It is that angle greater than 90º, but less than 180º.
  • Right angle: It is that angle that measures 90º.

Examples of convex angles

Let's look at some examples of convex angles:

  • The interior angles of a triangle are convex, since their sum must be equal to 180º.
  • If we have a clock and one of its handles points to 12 and the other to 4, both handles form a convex angle.
  • If a person opens his legs, without being able to reach the floor, he is forming a convex angle with both.

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