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13 March, 22:53

An interior angle of a regular convex polygon is 135 degrees. How many sides does the polygon have?

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  1. 13 March, 22:58
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    The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of sides. Then you would divide the sum by the number of sides to find what one angle is.

    Knowing the angle you can calculate n (number of sides):

    (n-2) * 180 / n = 135

    Use distributive property:

    180n - 360 / n = 135

    Multiply both sides by n:

    180n - 360 = 135n

    add 360 to both sides:

    180n = 135n + 360

    Subtract 135n from both sides:

    45n = 360

    Divide both sides by 45:

    n = 360 / 45

    n = 8

    The polygon has 8 sides.
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