Question

If a polygon has $6$5 diagonals, then the number of sides of the polygon is

• A. $25$
• B. $20$
• C. $15$
• D. $13$

Answer 1

The correct option is D $13$

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 65 diagonals so

$\frac{n(n-3)}{2}$ = 65

$n=13$

So we have 13 vertices hence 13 sides.