Exterior Angles of Polygons--Proofs without Words
- Tim Brzezinski
Choose any polygon of your choice on the right side of the screen. Polygons range from n = 3 (a triangle) to n = 8 (octagon). You can only select one polygon at a time. This applet displays the EXTERIOR ANGLES of a polygon you select (on the right side of the screen.) These exterior angles are shown in different colors.
Notice how the "Triangle" (polygon) is selected. 1) Click the check-boxes (one next to each exterior angle) to copy these angle measures to move them to another location on your screen. 2) Drag the vertices of the triangle around afterwards. What do you ALWAYS notice about the exterior angles of this polygon? Explain. Now select "Quadrilateral". Repeat steps (1) & (2) above for the quadrilateral. Repeat steps (1) & (2) for the pentagon, hexagon, heptagon, and octagon. Does it seem like we can make a general conclusion about the exterior angles of a polygon? If so, describe in detail.