Question

Sum of the interior angles of a regular polygon is ${1620}^{\circ }$. How many sides does this polygon have?

Answer 1

$\Rightarrow$Sum of interior angles $\left(A\right)=(n-2)\times {180}^o$

$\Rightarrow$ ${1620}^o=(n-2)\times {180}^o$

$\Rightarrow$ $\frac{{1620}^o}{{180}^o}=n-2$

$\Rightarrow$ $9=n-2$

$\Rightarrow$ $n=9+2$

$\therefore$ $n=11$

$\therefore$ Polygon has $11$ sides.