Question
The interior angles of a polygon are in AP. If the smallest angle is 120∘ and the common difference is 5∘, then find the possible number of sides of that polygon?
Answer: Option B
:
B
Sum of the interior angles of a polygon = (n-2) 180
n2 * (2a+ (n-1)d)= (n-2)180
n2* [2*(120) + (n-1)5]=(n-2)180
n[48+(n-1)] = (n-2)72
n2 -25n + 144=0
n=9 and n=16
when n= 16, the greatest angle will be equal to a+15d = 120 + 15 x 5 = 195 and no interior angle of a
polygon can be equal to or greater than 180. hence answer =b
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:
B
Sum of the interior angles of a polygon = (n-2) 180
n2 * (2a+ (n-1)d)= (n-2)180
n2* [2*(120) + (n-1)5]=(n-2)180
n[48+(n-1)] = (n-2)72
n2 -25n + 144=0
n=9 and n=16
when n= 16, the greatest angle will be equal to a+15d = 120 + 15 x 5 = 195 and no interior angle of a
polygon can be equal to or greater than 180. hence answer =b
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