Equiangular polygon


A polygon is one whose interior angles have the same measure, being these angles those that are formed from two segments of the figure.

Seen in another way, the equiangular polygon is a regular polygon if it is true that all the sides of the figure are of the same length, that is, if the polygon is equilateral.

We must remember, at this point, that a polygon is a two-dimensional figure made up of consecutive segments (not collinear) that form a closed space.

Likewise, the interior angle of a polygon is one that is formed from the union of two of its sides and is located within the figure.

Some types of equiangular polygons

To understand it better, the square is an equiangular polygon because all its interior angles are right, that is, they measure 90º. Similarly, a rectangle is equiangular because all its interior angles are also right.

However, unlike the square, the rectangle is not a regular polygon because not all sides are identical.

Square Rectangle

Another case of an equiangular polygon is that of the equilateral triangle, where each interior angle measures 60º.

Equilateral triangle

Interior angle of an equiangular polygon

The interior angle of an equiangular polygon can be calculated with the following formula, where θ is the measure of the interior angle and n is the number of sides of the polygon.

Equiangular polygons practical example

Suppose we have a regular octagon. How long are each of its interior angles?

Remember that a regular polygon is equiangular and equilateral, that is, its interior angles and the length of its sides are equal to each other. Thus, we apply the formula presented above:

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