The Number of Sides of The Polygon is

The measure of each interior angle of a regular convex polygon is 156o. The number of sides of the polygon is

  1. 10
  2. 8
  3. 15
  4. 12
Monis Rasool Professor Asked on 20th September 2015 in Maths.
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  • 1 Answer(s)

    Answer: (3) 15

    Explanation:-
    Each interior angle of a regular convex polygon = 156o
    Formula-
    The sum of interior angles = (n – 2) 180

    Then, the each interior angle = (n – 2) x 180/n
    Where, n = number of the sides in the polygon.

    (n – 2) x 180/n = 156
    (n – 2) x 180 = 156 x n
    180 n – 360 = 156 n
    180n – 156n = 360
    24n = 360
    n = 360 /24
    n = 15

    Then, the number of sides in the polygon is 15.

    Hence, the answer is (3) 15.

    Anurag Mishra Professor Answered on 20th September 2015.
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