A connected planar graph $G$ has $20$ faces, and every vertex of $G$ has degree exactly $4$.
Find the number of vertices of $G$.
I thought I could probably use the equation that goes like $V+E = F+2$, and I'm pretty sure that the part about each vertex having degree $4$ is a hint on how to find the number of edges, but I'm not sure on how to how to get that.
If every vertex has degree $4$, that means if $V$ is the number of vertices, there are $E = 4V/2 = 2V$ edges. This is because for a given vertex, we can count $4$ edges incident to that vertex. But each edge connects exactly $2$ vertices.
The rest is a straightforward application of the equation $V + F = E + 2$.