Copy of Sum of the angles of a polygon (by breaking sides)
"Break" one or more sides of the triangle. Then expand the triangle. As the triangle expands note that the angles change, but the sum of the angles remains constant. Each "break" adds a vertex and adds an additional 180 degrees to the original 180 degrees of the triangle.
3 sides (3 angles) --> 180 degrees.
4 sides (4 angles) --> 2*180 degrees.
5 sides (5 angles) --> 3*180 degrees.
6 sides (6 angles) --> 4*180 degrees.
Note that the number of "180's" is two less than the number of sides, hence the formula, sum = (n-2)*180