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18 July, 00:22

The number of sides of a regular polygon whose interior angle is 140

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Answers (2)
  1. 18 July, 01:02
    0
    9

    Step-by-step explanation:

    The sum of the interior angle and the exterior angle = 180°

    Thus the exterior angle of the polygon = 180° - 140° = 40°

    The sum of the exterior angles of a polygon = 360°, thus

    number of sides = 360° : 40° = 9
  2. 18 July, 01:53
    0
    9 sides

    Step-by-step explanation:

    Two methods and the same answer = 9 sides

    Method 1: Since the interior angle 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.

    Method 2: Since the exterior angle 140 degrees, The sum of the interior angles = (2n - 4) * right angles. So 140n = (2n - 4) * right angles, or

    140n = (2n - 4) * 90, or

    140n = 180n - 360, or

    40n = 360, or

    n = 9 sides.

    Hence the number of sides is 9 sides.
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