Let $ABCDE$ be a convex lattice pentagon. Since the sum of the interior angles of a pentagon is $3\pi$, the sum of the $5$ pairs of adjacent interior angles is $6\pi$. Hence some pair of adjacent angles must sum to more than $\pi$. We may thus assume without loss of generality that $A + B> \pi$ (see figure 1-1). We may also assume that point $C$ is not further from line $AB$ than point $E$. Constructing parallelogram $ABCX$, we see that rays $AX$ and $CX$ lie inside angles $A$ and $C$ respectively. Thus point $X$ lies inside the pentagon. But if three vertices of a parallelogram are lattice points, the fourth vertex must also be a lattice point. Copy from: http://www.mathpropress.com/stan/bibliography/ngons.pdf