Find the number of diagonals of

For a diagonal to be formed, 2 vertices are required. Thus in a polygon, there are 10 sides. And no. of lines can be formed are ${ }^{n} C_{2}$, but in ${ }^{n} C_{2}$ the sides are also included. N of them is sides.

Thus the no. of diagonals are ${ }^{n} C_{2}-n$

(i) Hexagon

$\mathrm{N}=6$

so no of diagonal is ${ }^{6} \mathrm{C}_{2}-6$

$=9$

(ii) decagon

$N=10$

So no of diagonal is ${ }^{10} \mathrm{C}_{2}-10$

$=35$

(iii) $N=18$

So no of diagonal is ${ }^{18} \mathrm{C}_{2}-18$

$=135$