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GeoGebraGeoGebra Classroom

Angle Measures in Polygons

PART 1: 1.In each of the polygons, pick one vertex and draw all of the diagonals from that vertex. Notice how this divides each polygon into triangular regions 2.After you have drawn in all of the diagonals, complete the table on your worksheet. 3.Make a conjecture about the sum of the interior angles of any convex polygon. 4.Draw your own polygons of any size and test your conjecture!
PART 2: 1. Using the "Ray through 2 points" told, start at one vertex and extend a ray through the next vertex moving counterclockwise. Do this until the sides of the polygon are all extended by rays. 2. Using the "New Point" tool, plot a point on each of the rays that you have created on the figure- the points must be plotted on the ray outside of the polygon (do not place them on the polygon). 3. Using the angle tool, measure the exterior angles of the polygon, moving in a counterclockwise rotation. (To do this, you must select the 3 points that you want to make up the angle. Start by selecting one of the points that you plotted, then the two vertexes counterclockwise to that point.) 4. Record the number of sides of the polygon along with the measures of its exterior angles. 5. Find the sum of the interior angles of each polygon. 6. Make a conjecture about the sum of the exterior angles of a convex polygon. 7. How could we prove this?