Question

A polygon has 35 diagonals, then the number of its sides is

• A. 8
• B. 9
• C. 10
• D. 11

Answer 1

The correct option is C 10

Since ${}^n{C}_2-n=35\Rightarrow \frac{n!}{2!(n-2)!}-n=35$
$\Rightarrow n(n-1)-2n=70\Rightarrow n^2-3n=70$
$\Rightarrow n^2-3n-70=0\Rightarrow (n+7)(n-10)=0\Rightarrow n=10$