Question

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

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

Answer 1

The correct option is D ${162}^{\circ }$

interior angle $=\left(\frac{n-2}{n}\right){180}^{\circ }$

As ${144}^{\circ }=\frac{(n-2)}{n}{180}^{\circ }\Rightarrow n=10$

if sides are doubled then $n^1=20$

$\therefore$ integers angle $=\left(\frac{20-2}{20}\right){180}^{\circ }={162}^{\circ }$