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If a polygon of $n$ sides has 275 diagonals, then $n$ is equal to
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25
A polygon of $n$ sides has number of diagonals
$\begin{aligned} &=\frac{n(n-3)}{2}=275 \quad \text { [given] } \\ \Rightarrow \quad n^{2}-3 n-550 &=0 \Rightarrow(n-25)(n+22)=0 \\ \therefore \quad n &=25 & {[\because n \neq-22] }\end{aligned}$
$[\because n \neq-22]$
$\begin{aligned} &=\frac{n(n-3)}{2}=275 \quad \text { [given] } \\ \Rightarrow \quad n^{2}-3 n-550 &=0 \Rightarrow(n-25)(n+22)=0 \\ \therefore \quad n &=25 & {[\because n \neq-22] }\end{aligned}$
$[\because n \neq-22]$
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