91Ó°ÊÓ

The formula for the measure of each interior angle for a regular polygon is $\frac{\left(n-2\right)\mathbf{180}}{n}$.

The formula for the measure of each exterior angle for a regular polygon is$\frac{360}{n}$

As, the measure of each interior angle of a regular n-gon is x times that of an exterior angle.

The value of x in terms of is n given by:

$$\begin{gathered} \frac{\left(n−2\right)180}{n}=x×\frac{360}{n} \\ \left(n−2\right)180=x×360 \\ n−2=x×\frac{360}{180} \\ n−2=x×2 \\ \frac{n−2}{2}=x \end{gathered}$$

Therefore, the value of x in terms of n is $\frac{n−2}{2}$.

The value of x in terms of n is $\frac{n−2}{2}$.

The value of x will be an integer if the numerator of the expression$\frac{n−2}{2}$ is an even positive number.

As,the value of x will be an integer if the numerator of the expression$\frac{n−2}{2}$ is an even integer.

That implies$n−2$ must be an even positive integer.

Therefore, the value of n must be an even positive integer for x to be an integer.