Question

Choose the correct answer from the alternatives given.
Each interior angle of a regular polygon is ${144}^{\circ }$. The number of sides in the polygon is

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is C $10$

If the number of sides of the polygon be n.
According to the question.
Then, $\frac{(n-2)}{n}\times \left({180}^{\circ }\right)={144}^{\circ }$
$\Rightarrow \frac{n-2}{n}=\frac{144}{180}\Rightarrow 1-\frac{144}{180}=\frac{2}{n}\Rightarrow \frac{36}{180}=\frac{2}{n}$
$\Rightarrow n=2\times 5\Rightarrow n=20$
$\therefore$ $n=10$
Hence, the sides of polygon are $10$.