Exterior Angles

Find the total number of degrees in a polygon's exterior angles

Students had spent time discovering the relationship for the angles in any polygon by seeing that there were two less triangles in a polygon than the number of sides.

Now it was time to see what the relationship was for the exterior angles of a polygon.

	Students each select a polygon and drew it on plain paper.
	The students added exterior angles at each vertex.

The students cut off the exterior angles and rearranged them around a point.

WOW! Every time the students put their angles around the point the angles totaled to 360 degrees. It didn't matter how many sides the polygon had.

Therefore, the students conjectured that the sum of the exterior angles on any polygon would always be 360 degrees.

In addition to this activity the students concluded the period by walking 2 polygon which had been taped to the floor. (These were of interest when the students entered the room, but they did not why they were there.)

Students also look at proof by infinity by thinking about a series of pictures of the polygon decreasing in size to a dot. This showed the students that the polygon eventually disappeared and all that was left was the picture of their many angles coming together at a point. Again the total was 360 degrees.