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

Question

Aicharya · Accepted Answer

We know that, $\begin{array}{rlrl}	ext { Number of diagonals } & =\frac{n(n-3)}{2} \ & 	herefore & 170 & =\frac{n(n-3)}{2} \ \Rightarrow & 340 & =n(n-3) \ \Rightarrow & 20 	imes 17 & =n(n-3) \ \Rightarrow & n & =20\end{array}$

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

Solution