Polygon Angle Sums



Use the following applets to explore the properties of polygons and their angles. Record on a separate piece of paper observations and conjectures. Predict what the angles in each poylgon will sum to. Recall that the angles in any given triangle sum to 180 degrees.


    Some questions to consider:

• What patterns do you see?
• What relationship do you see between the number of sides and the number of possible triangles?
• What about between the number of possible triangles and the sum of the angles?
• What other relationships do you see?





Quadrilateral		Pentagon		Hexagon		Heptagon
Octagon		Nonagon		Decagon




(Hint: If you are having difficulties, try making sure your line segments for the triangles don't cross within the polygon)


Once you have checked your conjectures, come up with a formula to determine the sum of the angles in a polygon using 180 degrees and the number of sides in the polygon.


A regular polygon has all angles equal and all sides equal. How would you go about determining the measure of each angle in a regular polygon?

Determine what the measure of each individual angle will be for a regular pentagon (5 sides).

Determine what the measure of each individual angle will be for a regular hexagon (6 sides).

Determine what the measure of each individual angle will be for a regular heptagon (7 sides).

Determine what the measure of each individual angle will be for a regular octagon (8 sides).

Determine what the measure of each individual angle will be for a regular nonagon (9 sides).

Determine what the measure of each individual angle will be for a regular decagon (10 sides).

Now choose a regular polygon to construct using a protractor and a straight edge. Then use your creativity, as well as a straight edge, a compass, colored pencils, crayons and any other tools you can find to create a piece of art. It can be simple or complex, it's up to you. Keep in mind that symmetry tends to look better.

(If you don't have a protractor, GeoGebra can be used as well. However, try to refrain from using the regular polygon tool. You can use the angle construction tools combined with the line segment construction tools.)