Interior Angles of Polygons

3 Sided Polygon -- Triangle: Move around points A, B, and C. Test out four angle sums.

Triangle Interior Angle Sums

Write out the four sums in the space below in the form [math]m\angle A+m\angle B+m\angle C=Total[/math].[br]Be sure to include the total for each sum! The angle measures are written out in a starter equation already, so you can copy that part directly.

4-Sided Polygon -- Quadrilateral: Move around points A, B, C, and D. Test out four different angle sums.

Quadrilateral Interior Angle Sums

Write out the four sums below in the same format.

5-Sided Polygon -- Pentagon: Move around points A, B, C, D, and E. Test out four different angle sums.

Pentagon Interior Angle Sums

Write out the four interior angle sums below. Continue to use the same format.

6-Sided Polygon -- Hexagon: Move around points A, B, C, D, E, and F. Test out four interior angle sums.

Hexagon Interior Angle Sums

Write out the four interior angle sums you tested in the space below. You're going to keep using the same format.

7-Sided Polygon -- Heptagon/Septagon: Move around points A, B, C, D, E, F, G. Test out four angle sums.

Heptagon Interior Angle Sums

Write out the four interior angle sums below.

8-Sided Polygon -- Octagon: Move around points A, B, C, D, E, F, G, and H. Test out four interior angle sums.

Octagon Interior Angle Sums

Write out the four interior angle sums below.

9-Sided Polygon -- Nonagon: Move around points A, B, C, D, E, F, G, H, and I. Test out four angle sums.

Nonagon Interior Angle Sums

Write out the four sums below.

10-Sided Polygon -- Decagon: Move around points A, B, C, D, E, F, G, H, I, and F. Test out four interior angle sums.

Decagon Interior Angle Sums

Write the four interior angle sums below.

In Closing: Answer the following questions based on your work above.

What pattern do you see in the sums for each type of polygon?[br][br]What pattern do you see in the sums as the number of sides increases?[br][br]How might you generalize a rule for the interior angle sum for a polygon with any number of sides?