InterviewSolution
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InterviewSolution
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Interior angle of polygon are in A.P.If the smallest angle is `120^@` and the common difference is `5^@`, find the number of sides of polygon. |
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Answer» Sum of interior angles of a `n`-sided polygon is `(n-2)**180`. Now, we are given, angles are in AP such that , `a = 120 and d = 5` `:. n/2(2a+(n-1)d) = (n-2)180` `=> n/2(240+(n-1)5) = 180n-360` `=>n(235+5n) = 360n-720` `=>5n^2+235n-360n+720 = 0` `=>5n^2-125n+720 = 0` `=>n^2-25n+144 = 0` `=>n^2-16n-9n+144 = 0` `=>n(n-16)-9(n-16) = 0` `=>(n-16)(n-9) = 0` `n=16 and n = 9` So, number of sides in the given polygon can be `16` or `9`. |
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