Concave angle


The concave angle is one that measures more than 180º or π radians, that is, it is greater than a straight angle and less than a full 360º angle.

We can see in the lower part an example of a concave angle that measures 190º:

We must remember that an angle is that arc that is formed by the crossing of two rays, lines or segments.

Another concept that we must remember is that of concavity, which refers to a surface with a greater sinking in the central part than in its ends. We can think, for example, in the case of a plate where soup can be served or of a well dug in the ground.

The opposite of a concave angle is one that is convex, that is, it is less than 180º, but greater than a null angle.

In this sense, it is worth noting that when two rays share a point they form a concave angle and, at the same time, another convex angle, adding both 360º, as we can see in the figure below where the angle measuring 252.9º is concave and the which measures 107.1º is convex.

Another important fact to mention is that a concave angle cannot be straight (90º), neither acute (less than 90º) nor obtuse (greater than 90º and less than 180º).

Concave angles can be found in geometric figures. Thus, those polygons that have at least one interior angle greater than 180º are concave polygons (The only polygon that cannot be concave is the triangle because its three interior angles must add up to 180º).

Examples of concave angle

Let's look at some examples of concave angle.

  • Suppose we have a gable roof. In its upper part a concave angle is formed (and in the lower part, which is more closed, a convex angle).
  • If we have a cake and one third of it is consumed, the periphery of the cake will form a concave angle.
  • If we extend and raise our arms and leave them slightly below shoulder height, the arch that joins both arms above the individual's head forms a concave angle.

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