# Inside angle

The interior angle is that arc formed by two sides of a polygon, so that it is contained within the figure.

That is, the interior angle is that arc that is constituted by the intersection of two sides of the polygon, being located within it.

Each vertex of the polygon corresponds to an interior and an exterior angle, both of which are supplementary, that is, they add up to 180º.

For example, if the interior angle of a triangle is 50º, its corresponding exterior angle at that very vertex measures 130º.

At this point, we must remember that a polygon is a two-dimensional geometric figure formed by consecutive non-collinear segments, constituting a closed space.

It should be noted that if any of the interior angles of a polygon is greater than 180º or π radians, the polygon is concave. On the other hand, if all the interior angles are less than 180º, the polygon is convex (see image below).

Likewise, if all the interior angles of a polygon are equal, we are faced with an equiangular polygon.

Types of angles## Sum and measure of interior angles

To find out how much the interior angles of a simple polygon add up (its sides do not cross each other), we must follow the following formula.

In the image above, n is the number of sides of sides of the polygon and θ is the interior angle.

Likewise, having a regular polygon, which is one whose sides and interior angles measure the same, the measure of each interior angle can be calculated with this formula:

## Interior angle example

Suppose we are in front of a regular pentagon. How much will its interior angles add up to, and how much will each of those angles measure?

That is, the sum of the interior angles of a pentagon is 540º, and if the polygon is regular, each interior angle will measure 108º.

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