Question

If a polygon of $n$ sides has $275$ diagonals, then $n$ $=$

• A. $25$
• B. $35$
• C. $20$
• D. $15$

Answer 1

The correct option is A $25$

If a polygon has n vertices then it will have $n$ sides and for every vertices you can draw $n-3$ diagonals

So, total number of diagonals should be $n(n-3)$ but this will mean that we have counted a diagonal twice (once from that vertices and once to that vertices). So total number of Diagonals should be $\frac{n(n-3)}{2}$

Given that we have 275 diagonals so

$\frac{n(n-3)}{2}$ = 275

$\Rightarrow n=25$

So we have 25 vertices, hence 25 sides.