Question

Each interior angle of a n-sided regular polygon is ${162}^{\circ }$. FInd the interior angle of another polygon with 2n sides.

• A. ${171}^{\circ }$
• B. ${144}^{\circ }$
• C. ${54}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is A ${171}^{\circ }$

Each interior angle of a n-sided regular polygon is ${162}^o$
Each interior angle of a n-sided regular polygon = $\frac{{180}^o(n-2)}{n}$
Now,
$\frac{{180}^o(n-2)}{n}={162}^o$
${180}^{o}n-{162}^{o}n={360}^o$
${18}^{o}n={360}^o$
$n=20$
The interior angle of another polygon with 2n sides = 40 sides
The interior angle of polygon = $\frac{{180}^o(n-2)}{n}=\frac{{180}^o(40-2)}{40}={171}^o$