A regular polygon of $n$ sides has 170 diagonals, then $n$ is equal to

The number of diagonals in a polygon with $n$ sides is given by the formula $D = \dfrac{n(n-3)}{2}$.

Given that the number of diagonals is 170, we set up the equation:

$\dfrac{n(n-3)}{2} = 170$

$n(n-3) = 340$

$n^2 - 3n - 340 = 0$

To solve this quadratic equation, we find factors of -340 that sum to -3. These are -20 and 17.

$(n - 20)(n + 17) = 0$

This gives $n = 20$ or $n = -17$.

Since the number of sides $n$ must be a positive integer, we have $n = 20$.

Answer: 20