The sum of angles in a polygon

Here is a demonstration (not a proof) that the sum of interior angles in a particular triangle is 180 degrees.

Draw any triangle on a piece of paper, using a ruler; cut it out, making sure the sides are straight.
Choose the longest side of the triangle as the base. Fold the triangle on a line parallel to the base so that the top vertex lies on the base.
Now fold the triangle so that the right vertex touches the top vertex (in its folded down position). The two parts of the right side of the triangle should line up, and the right part of the bottom side should be folded along itself.
Fold in the left vertex in the same way. You should see the three interior angles of the triangle meeting at a point, forming an 180 degree angle with no overlapping.

Mathematical fact (also called a theorem): The sum of interior angles in any triangle is 180 degrees.

What about other polygons? (A polygon is a plane figure with straight sides, such as a triangle, square, or trapezoid.) For example, a square has four 90-degree angles, so the angle sum is 360^o. Check the angle sums for all the pattern blocks.

1. Find a pattern, rule, or formula for the sum of the interior angles in an n-gon (a polygon with n sides, where n is a positive whole number).
   

Number of sides in polygon	3	4	5	6	7	8	9	10	n
Sum of angles in polygon	180o	360	180o	360o ?	____	____	____	____	____	____	____

Hint: Draw line segments to divide an n-sided polygon into triangles. Add up the measures of all the angles in all the triangles, and compare with the angles in your polygon.

Definition: A regular polygon is a polygon whose sides all have the same length and whose angles all have the same measure.
Examples: Equilateral triangles and squares are regular polygons.

2. Find a formula for the measure of one angle in a regular n-gon. Use your answer to the previous question.