What is the Number of Sides of the Polygon? If

The ratio of each interior angle to each exterior angle or a regular polygon is 3:1. The number of sides of the polygon is:

  1. 8
  2. 9
  3. 6
  4. 7
Monis Rasool Professor Asked on 28th August 2015 in Maths.
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1 Answer(s)

Answer: (1) 8

Explanation:-
Formula-
Interior angle = (2n – 1) x 90/n
Where, n = number of side in a polygon.
Exterior angle = 360/n

According to the question,
Then, (2n – 4) x 90/360  = 3: 1
2n – 4/4 = 3/ 1
2n – 4 = 12
2n = 12 + 4
2n = 16
n = 16/2
n = 8
Then,the number of sides in the polygon is 8.

Hence, the answer is (1) 8.

 

Anurag Mishra Professor Answered on 2nd September 2015.
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