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How to Find the Number of Sides of a Polygon

by Chance E. Gartneer, Demand Media

    A polygon by definition is any geometric shape that is enclosed by a number of straight sides, and a polygon is considered regular if each side is equal in length. Polygons are classified by their number of sides. For example, a six-sided polygon is a hexagon, and a three-sided one is a triangle. The number of sides of a regular polygon can be calculated by using the interior and exterior angles, which are, respectively, the inside and outside angles created by the connecting sides of the polygon.

    Step 1

    Subtract the interior angle from 180. For example, if the interior angle was 165, subtracting it from 180 would yield 15.

    Step 2

    Divide 360 by the difference of the angle and 180 degrees. For the example, 360 divided by 15 equals 24, which is the number of sides of the polygon.

    Step 3

    Divide 360 by the amount of the exterior angle to also find the number of sides of the polygon. For example, if the measurement of the exterior angle is 60 degrees, then dividing 360 by 60 yields 6. Six is the number of sides that the polygon has.

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    Tip

    • Subtracting the interior angle from 180 gives the exterior angle, and subtracting the exterior angle from 180 gives the interior angle because these angles are adjacent.

    About the Author

    Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.

    Photo Credits

    • Liquidlibrary/liquidlibrary/Getty Images

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