RMM 2020 Problem 5

A lattice point in the Cartesian plane is a point whose coordinates are both integers. A lattice polygon is a polygon all of whose vertices are lattice points.

Let $\Gamma$ be a convex lattice polygon. Prove that $\Gamma$ is contained in a convex lattice polygon $\Omega$ such that the vertices of $\Gamma$ all lie on the boundary of $\Omega$ , and exactly one vertex of $\Omega$ is not a vertex of $\Gamma$ .