EDB — 29Z

[29Z]Difficulty:*.Let \(n≥ 3\) integer; consider a polygon of \(n+1\) vertices. Show that it can be cut in two polygons, one with \(h\) and one with \(k\) sides, and \(3≤ h≤ n\), \(3≤ k≤ n\). By "cut" we mean, two vertexes of the polygon (not contiguous) can be connected by a line that is internal and does not touch other vertexes or sides. The intersection of the two polygons is the segment \(BD\), they do not have other points in common.

Hint. there is at least one vertex \(B\) ”convex” in which the inner angle \(𝛽\) is “convex” (i.e. \(0{\lt}𝛽≤ 𝜋\) radians); call \(A,C\) the vertexes contiguous to \(B\); reason on the triangle \(ABC\).