An $n$-gon has angle sum $(n-2)180^\circ$. If this $n$-gon is regular each of its angles therefore is ${n-2\over n}180^\circ$. Since we want that an integer number $k$ of such regular $n$-gons meet at each vertex of the tessellation we have to insist that ${n-2\over n}180^\circ={1\over k}360^\circ$, or $$k={n\over n-2}\in{\mathbb N}\ .$$ Now try $n=3$, $4$, $5$, $\ldots$, and see in which cases the resulting $k$ is integer. You will obtain a finite list of admissible $n$s and then have to check for which of these $n$s a tessellation is indeed possible.