Concept Byte: Exterior Angles of Polygons

Use With Lesson 6-1

TECHNOLOGY

Activity

Construct Use geometry software. Construct a polygon similar to the one below. Extend each side as shown. Mark a point on each ray so that you can measure the exterior angles.

Investigate Use your figure to explore properties of a polygon.

• Measure each exterior angle.
• Calculate the sum of the measures of the exterior angles.
• Manipulate the polygon. Observe the sum of the measures of the exterior angles of the new polygon.

Exercises

1. Write a conjecture about the sum of the measures of the exterior angles (one at each vertex) of a convex polygon. Test your conjecture with another polygon.

2. Extend The figures below show a polygon that is decreasing in size until it finally becomes a point. Describe how you could use this to justify your conjecture in Exercise 1.

   

3. The figure below shows a square that has been copied several times. Notice that you can use the square to completely cover, or tile, a plane, without gaps or overlaps.

   

   1. Using geometry software, make several copies of other regular polygons with 3, 5, 6, and 8 sides. Regular polygons have sides of equal length and angles of equal measure.
   2. Which of the polygons you made can tile a plane?
   3. Measure one exterior angle of each polygon (including the square).
   4. Write a conjecture about the relationship between the measure of an exterior angle and your ability to tile a plane with the polygon. Test your conjecture with another regular polygon.

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