How would you define the exterior angles of a non convex quadrilateral ABCD so that the sum of the four exterior angles is 360
In any quadrilateral (whether convex or not) the interior angles add up to . This is because a diagonal can be drawn that divides the quadrilateral into two triangles. The sum of the angles of each triangle is . Therefore , where denote the interior angles at each vertex.
Then if we define the size of each exterior angle as minus the size of the interior angle, and denote the exterior angles by , we have:Grandad