Question

Each interior angle of a regular polygon is ${144}^0$. Find the interior angle of a regular polygon which has double the number of sides as the first polygon.

• A. ${100}^0$
• B. ${160}^0$
• C. ${36}^0$
• D. ${162}^0$

Answer 1

The correct option is D ${162}^0$

Since each interior angle of the first polygon $={144}^o$
Each exterior angle of the first polygon $=180-144$
$={36}^o$
$\therefore$ The number of sides of the first polygon $=\frac{360}{36}=10$
$\therefore$ The number of sides of the second polygon $=2\times 10=20$
$\therefore$ Each exterior angle of the second polygon $=\frac{{360}^o}{20}={18}^o$
$\therefore$ Each interior angle of the second polygon $={180}^o-{18}^o={162}^o$