Question 578764
the sum of the interior angles of a polygon can be found using the following formula:


sum of the interior angles of a polygon = (n-2) * 180
n is the number of sides of the polygon.


if the polygon is regular (all the angles are equal), then each angle can be found by dividing the sum of the angles of the polygon by the number of sides.


example:


assume there are 7 sides to the polygon.
the sum of the angles of this polygon would be (7-2) * 180 = 5 * 180 = 900.


if this 7 sided polygon were regular (all sides are equal and all angles are equal), then the measure of each angle would be 900 / 7 = 128.5714286.


if the 7 sides polygon were not regular, then each angle could be just about any measure as long as the sum was equal to 900.


a very good reference that allows you to play with the shape of the polygon can be found here:
<a href = "http://www.mathopenref.com/polygoninteriorangles.html" target = "_blank">http://www.mathopenref.com/polygoninteriorangles.html</a>


set the number of sides to 7 and you'll see that the sum is 900.
play with the shape of the polygon and each angle will change but the sum will remain at 900.
select on the make regular box and you'll see that each angle will be as stated above.
they seem too round the angles to the nearest integer so you'll get close but not right on if the angle is not an exact integer.