Question

Find the number of sides of a polygon, if the sum of its interior angles is:
${1620}^{\circ }$

Answer 1

Find number of sides

Let the number of sides of a polygon be $n$.
We know that,
Sum of interior angles $=(n-2)\times {180}^{\circ }$
Sum of interior angles of the given polygon $={1620}^{\circ }$
$\therefore {1620}^{\circ }=(n-2)\times {180}^{\circ }$
$(n-2)=\frac{{1620}^{\circ }}{{180}^{\circ }}$
$(n-2)=9$
$n=11$

Hence, the number of sides of the polygon is $11$.