Question

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

• A. ${155}^{\circ }$
• B. ${160}^{\circ }$
• C. ${171}^{\circ }$
• D. one of the above

Answer 1

Answer: (C)

${171}^{\circ }$

Each Angle of a $n$-sided Regular Polygon$=\frac{(n-2){180}^o}{n}$

Given interior Angle of a $n$-sided Regular Polygon$={162}^o$

So $\frac{(n-2){180}^o}{n}={162}^o$

$\Rightarrow (n-2)\times 90=81n$

$\Rightarrow 90n-81n=180$

$\Rightarrow 9n=180$

$\Rightarrow n=20$

So for $2n$ sides the interior Angle will be $=\frac{(2n-2){180}^o}{2n}=\frac{(n-1){180}^o}{n}=\frac{(20-1){180}^o}{20}=19\times 9={171}^o$