This GeoGebra applet illustrates a simple, general formula for the interior angle sum of polygons, namely, 180([i]n[/i]-2[i]k[/i]) which is valid also for [i]crossed polygons[/i], whereas the usual formula ([i]n[/i]-2)180 used at high school is restricted only to simple closed polygons (convex and concave). The following crossed polygons are dynamically illustrated: pentagon, septagon, octagon and quadrilateral.
A more detailed learning activity which starts with turtle geometry to develop the required concept of 'turning angle' (i.e. exterior angle) for understanding the general proof is available at: http://dynamicmathematicslearning.com/angle-sum-student-explore.html