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(Q). A polygon has 65 diagonals then find its number of sides.
Solution:-
Let number of sides = n
∴ number of vertices = n
⟹ ⁿC₃ – n = 65
⟹  \frac{{n(n - 3)}}{2} = 65
⟹ n(n-3) = 2×5×13
      n(n-3) = 13(13 – 3)

∴ n = 13           Answer