The sum of the measures of the angles of a triangle is 180°. Consider each convex polygon with all possible diagonals drawn from one vertex. In each case, the polygon is cut into triangles. The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of the dissected triangles. Complete the table below.

1. Is there a connection between the number of sides and the number of dissected triangles in a polygon? What is this relation?

2. How many dissected triangles are there in an n-sided polygon? What is the sum of the interior angles of an n-sided polygon?

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