Question

A polygon has $35$ diagonals. The number of sides of polygon is

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is C $10$

We know that, the number of diagonals $=\frac{n(n-3)}{2}$
(where $n=$ number of sides of polygon)
Here, $\frac{n(n-3)}{2}=35$
$\Rightarrow n(n-3)=70$
$\Rightarrow n^2-3n-70=0$
$\Rightarrow (n-10)(n+7)=0$
$\Rightarrow n=10$ or $-7$
Since, number of sides can not be negative.
So, it has $10$ sides.