Question

A polygon has 44 diagonals, then the number of its sides are

• A. 11
• B. 7
• C. 8
• D. None of these

Answer 1

The correct option is A 11

Let there be n sides of the polygon. Then it has n vertices.
The total number of straight lines obtained by joining n vertices by taking 2 at a time is $n_{C_2}$.
These $n_{C_2}$ lines also include n sides of the polygon.
Therefore, the number of diagonals formed is $n_{C_2}-n$.

Thus, $n_{C_2}-n=44$
$\Rightarrow \frac{n(n-1)}{2}-n=44$
$\Rightarrow \frac{n^2-3n}{2}=44$
$\Rightarrow n=11$
Verify by actual substitution.