Find the number of diagonals of (i) a hexagon (ii) a polygon of 16 sides.

(i) hexagon $\to$ A hexagon has 6 angular points. By joining any two angular points we get a line which is either a side or a diagonal.

$\therefore$ Number of lines ${}^6{C}_2=\frac{6!}{2!4!}$

$=\frac{6\times 5}{2}=15$

Number of sides = 6

$\therefore$ Number of diagonals = 15 - 6 = 9

(ii) Polygon of 16 side will have 16 angular points. By joining any 2 points we get a line which is either a side or a diagonal.

$\therefore$ number of lines ${=}^{16}{C}_2=\frac{16!}{2!4!}$

$=\frac{16\times 15}{2}=120$

$\Rightarrow$ number of sides = 16

$\therefore$ number of diagonals = 12 - 16 = 104