The sum of the angle measures of a polygon with n sides is 3960 . Find n

Answer 1

Here is how to visualize this kind of problem:

To walk around any polygon, you will make a series of turns. Start with a square: to get from one corner back to the same point, you will make 3 90-degree turns. This means you have gone "around a corner" that has an angle of 90 degrees. You do this 3 times for a 4-sided square (or rectangle. The turns need to add up to 360 degrees (because you wind up travelling in the same direction you started.)

So--for the square--the angle (A) is 90 degrees. Each turn is 180 - A, and the number of turns (N) is the same as the number of sides to the figure.

So--(180 - A)*N = 360

180 - A = 360 / N

A = 180 - 360 / N

Test it for the square: A = 180 - 360 / 4 = 90

Answer 2

3960 = (n - 2)(180) This is a given formula

Can you solve for n and answer?