General formula interior angle sum polygons (incl. crossed)

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:

Visit: http://dynamicmathematicslearn…r_pentagon.html


Resource Type
exterior-angle  interior-angles  polygon  turning-angle 
Target Group (Age)
14 – 19+
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