Graph Theory, planar graph $(p,q)$ is in the form $q=\frac{n(p − 2)}{(n − 2)}$where $q$- #edges, $p$- #points

Question

If $G$ is a $(p, q)$ planar graph with every face being a $n$-cycle then $$q=\frac{n(p − 2)}{(n − 2)}$$where $q$- #edges, $p$- #points.

I tried using the Euler formula, which states:

$p-q+f=2$, hence, I need to find the number of faces (f) such graph has. I tried saying $f=q/n$ but it doesn't yield the result.

Answer 1

Using degree sum formula,

$$\sum r(e)=\sum r(f)\iff \sum_{edges} 2=\sum_{faces} n$$

Rearranging and plugin into $p-q+f=2$ yields the result.