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A regular polygon of $n$ sides has 170 diagonals, then $n$ is equal to
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The correct answer is:
$20$
We know that,
$\begin{array}{rlrl}\text { Number of diagonals } & =\frac{n(n-3)}{2} \\ & \therefore & 170 & =\frac{n(n-3)}{2} \\ \Rightarrow & 340 & =n(n-3) \\ \Rightarrow & 20 \times 17 & =n(n-3) \\ \Rightarrow & n & =20\end{array}$
$\begin{array}{rlrl}\text { Number of diagonals } & =\frac{n(n-3)}{2} \\ & \therefore & 170 & =\frac{n(n-3)}{2} \\ \Rightarrow & 340 & =n(n-3) \\ \Rightarrow & 20 \times 17 & =n(n-3) \\ \Rightarrow & n & =20\end{array}$
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