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Question

In a polygon, the interior angles are in A.P. with common difference 5 and smallest angle 120, then the number of sides is :


  1. 9 or 16

  2. 25

  3. 16

  4. 9


Solution

The correct option is D

9


Let number of sides of polygon = n.

∴ Sum of internal angles = 180n - 360.

∴ 180n - 360 =  n2[240 + (n-1)5]

n2 - 25n + 144 = 0 ⇒ n = 16 or 9.

Since internal angle of a polygon <  180.

T16   = 120 + 15 × 5 = 195 > 180 ⇒ n ≠ 16.

Hence n = 9.

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