Let n be the number of sides of a polygon and D be the number of diagonals of that polygon
We know that, D = \(n_{c_2}\) - n = \(\frac{n(n-3)}{2}\)
∴ 35 = \(\frac{n^2-3n}{2}\)
⇒ n2 − 3n − 70 = 0
⇒ (n − 10)(n + 7) = 0
⇒ n = 10, −7
Since, sides cannot be negative, therefore n = 10.
Hence, polygon is a decagon.