Question

The number of diagonals in a polygon is $20$. The number of sides of the polygon is

• A. $5$
• B. $6$
• C. $8$
• D. $10$

Answer 1

Answer: (C)

$8$

Let $n$ be a side of polygon
Then, number of diagonals of the polygon
$={{}^{n}C}_2-n$
$\Rightarrow 20=\frac{n(n-1)}{2}-n$
$\Rightarrow n^2-3n-40=0$
$\Rightarrow (n+5)(n-8)=0$
$\Rightarrow n=8$ ($\because$ $n$ cannot be negative)