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Maths Exercices

Equiangular polygon Sums

Polygons in general...

  • An equilateral polygon is a polygon with all sides congruent.
  • An equiangular polygon is a polygon with all angles congruent.
  • A regular polygon is a polygon that is both equilateral and equiangular.
Equilateral Polygon
Equiangular Polygon
Regular Polygon

Sum of the interior angles of a equiangular polygon
The sum of the angles in a polygon is always equal to the number of sides in a polygon minus two, all multiplied by 180. That is,

angles sum = (n-2)·180º


Measure of one angle in any equiangular or regular polygon.
Since the angles in an equiangular polygon or regular polygon are equal, the measure of one angle in any equiangular or regular polygon is simply the sum of polygon angles divided by the number of angles in the polygon.

What is the measure of one angle in a regular nonagon?