Exploring Equiangular Polygons: Properties, Formulas, And Symmetry

Equiangular Polygon

a polygon where all the angles have the same measure

An equiangular polygon is a polygon in which all of its interior angles are congruent or equal. In other words, each angle inside the polygon has the same measure. Examples of equiangular polygons include equilateral triangles, squares, regular pentagons, regular hexagons, and regular octagons.

Equiangular polygons have some interesting properties because of their angles. For instance, in an equiangular polygon with n sides (n-gon), each angle measures (n-2) * 180 / n degrees. Hence, the sum of all interior angles in an n-gon polygon is (n-2) *180 degrees. This formula can help calculate the number of sides in an equiangular polygon given the measure of one of its angles or vice versa.

Moreover, equiangular polygons are symmetrical about their center, which means that the lines connecting the center of the polygon to the vertices of the polygon are congruent in length. This leads to other remarkable properties like regularity, convexity, and the fact that the apothem (distance from the center to any side of the polygon) is the same for all sides.

In summary, equiangular polygons are fascinating geometric figures that have equal interior angles, and they have unique properties that arise due to this characteristic, such as their symmetrical center, regularity, and congruent apothems.

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