What is the sum of the interior angles on a polygon that has 4 diagonals at each vertex?

uming the polygon is convex, if there are 4 diagonals then there must be 4+2=6 points other than the vertex being considered (2 points are adjacent, so lines to them are not diagonals), hence there are 7 vertices and 7 sides. the exterior angles add up to 360 degrees so the interior angles add up to 7*(180-360/7)=(7*180)-360 degrees.