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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