Question

Fill in the blanks:​
(vi)

Answer 1

Given : Each interior angle is ${165}^{\circ }$
Let each exterior angle be $x$.

Now, $\text{Each exterior angle}+\text{Each interior angle}={180}^{\circ }$

$\therefore$ ${165}^{\circ }+x={180}^{\circ }$

$x={180}^{\circ }-{165}^{\circ }$

$={15}^{\circ }$
So, each exterior angle is ${15}^{\circ }$

Also , each exterior angle $=\frac{{360}^{\circ }}{n}$

${15}^{\circ }=\frac{{360}^{\circ }}{n}$

$\therefore$ $n=\frac{{360}^{\circ }}{{15}^{\circ }}$

$\therefore$ $n=24$

So ,the number of sides is $24$.