Question

State true or false:

Is it possible to have a regular polygon whose exterior angle is $40\%$ of a right angle?

• A. True
• B. False

Answer 1

The correct option is A True

$40\%$ of a right angle will be,

${90}^{\circ }\times \frac{40}{100}={36}^{\circ }$

For a $n$-sided regular polygon all exterior angles are equal to $\frac{{360}^{\circ }}{n}$. So,

$\begin{array}{cc}{36}^{\circ }& =\frac{{360}^{\circ }}{n}\\ n& =\frac{{360}^{\circ }}{{36}^{\circ }}\\ & =10\end{array}$

We obtain an integral positive value of $n$ so, the given statement is true for a regular $10$-sided polygon.