. A polygon has 44 diagonals, the number of its sides, is 

Let there be n sides of the polygon.Then, it has. vertices. The total number of 

straight lines obtained by joining $n$  vertices by taking 2 at a time is  ${ }^n{C}_2\text{.}$

These  ${ }^n{C}_2$  2 lines also  nclude  $n$  sides of the polygon. Therefore, the number 

of diagonals formed is   ${ }^n{C}_2-n$

Thus, we have  

   $\Rightarrow n_{c_2}-n=44\Rightarrow \frac{n^2-3n}{2}=44\Rightarrow n=11$