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the interior angles fo a polygon are inarithmatic progration.The smallest angle is 120 degree and the common difference is 5 degree.Find the number of sides?

the interior angles fo a polygon are inarithmatic progration.The smallest angle is 120 degree and the common difference is 5 degree.Find the number of sides?

Grade:11

1 Answers

Pratyush Ranjan Roul
19 Points
7 years ago
the sequence seems to be 120, 125, 130 …..........
So,
Sn=n/2{ 240 + (n-1)5 }-----------------(i)
but the angles can never be 180o as it does not form a vertex and hence no side
So, it extend upto 175o
Sn also equals to  n/2{a + an}
Sn=n/2{120 + 175}--------- (ii)
Equating i and ii,
295 = 240 + 5n – 5
=> 5n = 60
=> n = 12
 

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