Understanding Equiangular Polygons | Properties and Formulas

equiangular polygon

An equiangular polygon is a polygon in which all angles are congruent or equal

An equiangular polygon is a polygon in which all angles are congruent or equal. In other words, each interior angle of the polygon has the same measure. For example, in an equiangular triangle, all three angles are 60 degrees.

In general, the sum of the interior angles of any polygon can be found using the formula: (n-2) × 180 degrees, where n represents the number of sides or vertices of the polygon. For an equiangular polygon, since all angles are equal, we can divide the total sum of the interior angles by the number of angles to find the measure of each angle.

For example, let’s consider an equiangular pentagon. A pentagon has 5 sides, so using the formula, the sum of the interior angles would be (5-2) × 180 = 3 × 180 = 540 degrees. Since it is equiangular, each angle would measure 540/5 = 108 degrees.

Equiangular polygons have some interesting properties. For instance, all equilateral polygons (polygons with all sides congruent) are also equiangular. This is because if all sides of a polygon are equal, the angles opposite those sides will also be congruent due to the properties of triangles formed by connecting the vertices to the center.

In summary, an equiangular polygon is a polygon where all angles are congruent. The measure of each angle can be found by dividing the sum of the interior angles by the number of angles in the polygon. It is worth noting that equiangular polygons typically have other properties, such as having all sides congruent in the case of equilateral polygons.

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