Q.

In a polygon, the interior angles are in A.P. with common difference 50  and smallest angle 1200 , then the number of sides is:

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a

9  or  16

b

16

c

9

d

None

answer is C.

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Detailed Solution

Let the 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<1800. T16=120+15×5=195>1800⇒n≠16 Hence n=9
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