Understanding Equiangular Polygons: Measures of Interior Angles and their Calculation

equiangular polygon

An equiangular polygon is a polygon where all the interior angles are congruent (i

An equiangular polygon is a polygon where all the interior angles are congruent (i.e., equal in measure). In other words, each angle inside the polygon has the same size.

To find the measure of each angle in an equiangular polygon, you can divide the sum of all the interior angles by the total number of angles (which is equal to the number of sides of the polygon).

The formula to find the sum of interior angles in a polygon is given by (n – 2) * 180 degrees, where n represents the number of sides/angles in the polygon. For example, for a triangle (n = 3), the sum of interior angles is (3 – 2) * 180 = 180 degrees. For a quadrilateral (n = 4), it is (4 – 2) * 180 = 360 degrees.

To find the measure of each angle in the equiangular polygon, you can use the formula: (sum of interior angles) / (number of angles). Let’s denote the measure of each angle as x.

So, x = (sum of interior angles) / (number of angles).

For example, let’s say we have an equiangular pentagon. In this case, n = 5, and the sum of interior angles would be (5 – 2) * 180 = 540 degrees. To find the measure of each angle, we divide the sum by the number of angles: x = 540 / 5 = 108 degrees.

Therefore, in an equiangular pentagon, each angle measures 108 degrees.

It is important to note that equiangular polygons are not necessarily regular polygons. Regular polygons have both equal angles and equal side lengths, while equiangular polygons only have equal angles.

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