Question

The number of diagonals of a polygon of $20$ sides is

• A. $210$
• B. $190$
• C. $180$
• D. $170$

Answer 1

Answer: (D)

$170$

Answer 2

Number of diagonals in a polygon of n sides
${{=}^{n}}{{C}_{2}}-n$
Here, $n=20$
$\therefore$ Required number of diagonals
${{=}^{20}}{{C}_{2}}-20$
$=\frac{20\times 19}{2\times 1}-20$
$=170$