Three, take $m$ points randomly inside a convex $n$-sided polygon, and connect these $m+n$ points (the $m$ points taken and the original $n$ vertices) in such a way that no two connecting lines intersect, and all regions in the figure are triangles. How many triangles are there in the figure?
Three, Prompt: The angles in the figure consist of two parts, one part of the angle has the vertex at the vertex of an $n$-sided polygon, and the other part of the angle has the vertex at $m$ points. According to this, calculate the degree of the angle, and argue that there are $(2m+n-2)$ triangles in the figure.