regular polygon
a polygon with all sides equal and all angles equal
A regular polygon is a closed two-dimensional figure with straight sides that has equilateral sides and equal interior angles. In other words, all sides of a regular polygon are of equal length and all of its interior angles are of equal measure.
The name of the polygon is derived from the number of sides it has. For example, a regular polygon with three sides is called an equilateral triangle, with four sides is called a square, with five sides is called a pentagon, and so on.
To find the measure of each interior angle of a regular polygon, we use the formula:
Interior angle measure = (n-2) * 180 / n
where n is the number of sides in the polygon. For example, a regular pentagon has five sides, so its interior angle measure would be:
(5-2) * 180 / 5 = 108 degrees
Similarly, we can find the measure of each exterior angle by using the formula:
Exterior angle measure = 360 / n
Regular polygons have several interesting properties, such as:
– All interior angles of a regular polygon are greater than 0 degrees and less than 180 degrees.
– The sum of the interior angles of a regular polygon with n sides is (n-2) * 180 degrees.
– The sum of the exterior angles of any polygon, regular or irregular, is always 360 degrees.
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