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## Answers

where n=no. of sides of the polygon.

so according to question:

27={n(n-3)}/2

=>54=n^2-3n

solving this equation we get n=9

hence no. of sides of the polygon=9

therefore 27 = C(n,2)

n(n-1)/2 -n =27

n∧2 -3n -54 =0

from above we get two values of n -6 and 9

no of sides cant we negative so 9 is the answer.

or you can simply solve by

n(n-3)/2 = no of daigonals