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If the number of diagonals of a regular polygon is 35 , then the number of sides of the polygon is
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Verified Answer
The correct answer is:
10
The number of diagonals of a regular polygon having $n$ sides is given by $\frac{n(n-3)}{2}$.
$$
\begin{aligned}
& \therefore \quad \frac{n(n-3)}{2}=35 \\
& \Rightarrow \quad n^2-3 n-70=0 \\
& \Rightarrow \quad n^2-10 n+7 n-70=0 \\
& \Rightarrow \quad n(n-10)+7(n-10)=0 \\
& \Rightarrow \quad(n-10)(n+7)=0 \\
& \Rightarrow \quad n=10,-7 \\
& \therefore \quad n=10 \\
&
\end{aligned}
$$
$$
\begin{aligned}
& \therefore \quad \frac{n(n-3)}{2}=35 \\
& \Rightarrow \quad n^2-3 n-70=0 \\
& \Rightarrow \quad n^2-10 n+7 n-70=0 \\
& \Rightarrow \quad n(n-10)+7(n-10)=0 \\
& \Rightarrow \quad(n-10)(n+7)=0 \\
& \Rightarrow \quad n=10,-7 \\
& \therefore \quad n=10 \\
&
\end{aligned}
$$
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