Question

A regular polygon has 27 diagonal. Find the number of sides in the regular polygon.

Answer 1

Answer:

Let the number of sides be n.

Number of diagonal in a polygon = n(n - 3) / 2

=> 27 = n( n - 3) / 2

=> n^2 - 3n - 54 = 0

=> n^2 + 6n - 9n - 54 = 0

=> n(n + 6) - 9(n + 6) = 0

=> (n - 9)(n + 6) = 0

=> (n - 9) = 0

=> n = 9

Therefore this polygon has 9 sides.

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