Question

A polygon has $35$ diagonals. The number of its sides are

• A. 8
• B. 9
• C. 10
• D. 11

Answer 1

The correct option is C 10

Number of diagonals in any $n$ sided polygon is $=$ Total Number of Lines connected two points $-$ Total number of sides of polygon.

So we have $n$ points so total number of lines is ${=}^n{C}_2$, because we have to choose two points from $n$ points.

Total number of sides $=$ $n$

So Number of diagonals$=\frac{n(n-1)}{2}-n$

Number of diagonals$=\frac{n(n-3)}{2}$

So we have number of diagonals $=35$

$\Rightarrow \frac{n(n-3)}{2}=35$

$\Rightarrow n(n-3)=70$

$\Rightarrow n=10$