Question

Fill in the blanks:

Number of sides	Each exterior angle	Each interior angle
	${36}^{\circ }$

Answer 1

Given: Each exterior angle $=\frac{{360}^{\circ }}{n}$
$\therefore {36}^{\circ }=\frac{{360}^{\circ }}{n}$
$\Rightarrow n=\frac{{360}^{\circ }}{{36}^{\circ }}$
$\therefore n=10$
So, the $\text{Number of sides}\left(n\right)=10$
We know that , each interior angle $=\frac{(n-2)\times {180}^{\circ }}{n}$
$=\frac{(10-2)\times {180}^{\circ }}{n}=\frac{8\times {180}^{\circ }}{10}=\frac{{1440}^{\circ }}{10}$

$\therefore \text{Each interior angle}={144}^{\circ }$