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19 March, 15:38

Each interior angle of a regular polygon is 140°. Find the number of sides of the polygon.

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  1. 19 March, 15:46
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    9 sides

    Explanation:

    Step 1

    Since the interior angle is 140 degrees, the supplement of this is the exterior angle and equal to 40 degrees. Hence the number of sides is 360/40 = 9 sides.

    Step 2

    Method 2: Since the exterior angle is 140°

    The sum of the interior angles = (2n - 4) * right angles.

    So 140n = (2n - 4) * right angles, or we can also say

    140n = (2n - 4) * 90

    140n = 180n - 360

    40n = 360

    Divide both sides of the equation by 40

    n = 9 sides.

    n = 9 sides. Hence the number of sides is 9 sides.
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