Question

Two regular polygons are such that the ratio of the measures of their interior angles is $4:3$ and the ratio between their number of sides is $2:1.$ Find the number of sides of each polygon.

Answer 1

Let number of sides of two polygons are $n$ and $2n$

measures of interior angles of x sided regular polygon is $\frac{(x-2)\times 180°}{x}$

so $\frac{\frac{2n-2}{2n}\times 180°}{\frac{n-2}{n}\times 180°}=\frac{4}{3}\Rightarrow \frac{2n-2}{2(n-2)}=\frac{4}{3}\Rightarrow 6n-6=8n-16\Rightarrow 2n=10\Rightarrow n=5$

Therefore, number of sides of polygon are 5 and 10.