Review:

1.) We know the interior angles of a triangle add up to _____ degrees.

2.) We also know that the interior angles of a quadrilateral add up to _____degrees.

3.) What about the interior angles of a 2-sided figure? Try to draw this or take a minute and try on geometer's sketchpad.

Let's make a table:

Number of Sides	Name of Polygon	Sum of Interior Angles
3	Triangle	180 degrees
4	Quadrilateral	360 degrees
5
6
7
8
9
10
12
n-sides

Can you fill in the rest of the table? For a hint, rewrite the table with 1 more column to find a pattern. The rewritten table is below to help you.

Number of Sides	Name of Polygon	Sum of interior angles	Rule
3	Triangle	180 degrees	1 x 180
4	Quadrilateral	360 degrees	2 x 180
5
6
7
8
9
10
12
n-sides

Do you see the pattern now? Here is the finished table with the established generalization:

**The students should see the pattern of numbers from the 1st column to the 4th column.

Number of Sides	Name of Polygon	Sum of interior angles	Rule
3	Triangle	180 degrees	1 x 180
4	Quadrilateral	360 degrees	2 x 180
5	Pentagon	540 degrees	3 x 180
6	Hexagon	720 degrees	4 x 180
7	Heptagon	900 degrees	5 x 180
8	Octagon	1080 degrees	6 x 180
9	Nonagon	1160 degrees	7 x 180
10	Decagon	1440 degrees	8 x 180
12	Dodecagon	1800 degrees	10 x 180
n-sides	n - gon		(n - 2)180

The first theorem has been established: The sum of the measures of the interior angles of any polygon can be found using the formula:

Where are the exterior angles of a polgon located?

What do you think their sum is?

Measuring in geometer's sketchpad, we get that the exterior angles of a triangle add up to 360 degrees.

Assignment #1: Use GSP to find what the exterior angles of other polygons add up to. Use the same table from above and come up with a generalization.

Remember that if a polygon is REGULAR, all sides are congruent and all angles are congruent.

So, could we find the measure of each interior angle of a regular hexagon?

1.) We need to find what the interior angles of a pentagon add up to.

We could look at our chart or quickly calculate (6-2)180 = 720 degrees.

2.) Since each angle is equal, 720 is split into 6 equal parts. So, 720/6 = 120 degrees is the measure of each interior angle.

Let's look at a sketch and measure to make sure!

So, we can see that each individual angle measures 120 degrees and that the sum is 720 degrees.

Assignment #2:

1.) Will all of the angles of every hexagon be 120 degrees?

Draw some pictures and explain your answers.

2.) Make a chart for the measure of each interior angle of all of the polygons that we did above and come up with a generalization.

3.) Do the same type of investigation for the measure of each exterior angle of a regular polygon. Is there a generalization for that?

GO straight to section 2!

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