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A well known Euler's formula consequence's corollary in graph theory statesthat: For a connected simple planar graph with $n$ vertices and $m$ edges, andgirth $g$, we have $m \leq \frac{g}{g-2}(n-2)$. We show that a connected simpleplane graph with $n$ vertices and girth $g$, and exterior face of degree $h$has at most $\frac{g}{g-2}(n-2)- \frac{1}{g-2}(h-g)$ edges. A \emph{convex hull$g$-angulation} is a connected plane graph in which the exterior face is asimple $h$-cycle and all inner faces are $g$-cycles. For a given set $S$ of $n$point in the plane having $h$ points in the boundary of its convex hull, wepresent the necessary and sufficient condition to obtain a convex hull$g$-angulation on $S$. We also determine the number of edges and inner faces inthe convex hull $g$-angulation.

On the maximum number of edges in plane graph with fixed exterior face degree