Question

The ratio between the number of sides of two regular polygons is 1:2 and the ratio between their interior angles is 2:3. The number of sides of these polygons are respectively.

Answer 1

We've got $n_{1}:n_{2}=1:2$ and $\frac{n_{1}-2}{n_{1}}:\frac{n_{2}-2}{n_{2}}=2:3$.
You get two equations, $2n_{1}-n{2}=0; 3n_{1}-n_{2}-4=0$
On solving them you get, $n_{1}=4$ and $n_{2}=8$
Hence, the figures are Square and Octagon.