equiangular polygon
An equiangular polygon is a polygon in which all of its interior angles are congruent, or equal in measure
An equiangular polygon is a polygon in which all of its interior angles are congruent, or equal in measure. In other words, each angle in an equiangular polygon has the same size.
For example, a regular pentagon is an equiangular polygon because all its interior angles measure 108 degrees. Similarly, a regular hexagon is an equiangular polygon because each interior angle measures 120 degrees.
It’s important to note that not all equiangular polygons are regular polygons. A regular polygon is a special case of an equiangular polygon in which all sides are congruent in length as well.
To determine the measure of each interior angle in an equiangular polygon, we can use the formula:
Interior angle = (n-2) * 180 / n
Here, “n” represents the number of sides in the polygon. For example, if we have a heptagon (a polygon with 7 sides), we can use the formula to find the measure of each interior angle:
Interior angle = (7-2) * 180 / 7 = 900 / 7 ≈ 128.57 degrees
Therefore, each interior angle in a heptagon measures approximately 128.57 degrees, making it an equiangular polygon.
Equiangular polygons are interesting because they have certain properties related to their angles. For instance, the sum of all the interior angles in an equiangular polygon can be found using the formula:
Sum of interior angles = (n-2) * 180 degrees
So for the heptagon example, the sum of the interior angles would be:
Sum of interior angles = (7-2) * 180 = 5 * 180 = 900 degrees
Equiangular polygons can have different numbers of sides, making them versatile geometric shapes.
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