SOLUTION: how would you find the value of an angle inside a polygon?

Question 578764: how would you find the value of an angle inside a polygon?
Found 3 solutions by dfrazzetto, scott8148, Theo:
Answer by dfrazzetto(283)   (Show Source): You can put this solution on YOUR website!
If its a regular polygon the total internal angles sum:
(S-2)180, where s is the number of sides
for a triangle s = 3, rectangle s=4, pentagon s=5, etc
Once you have the sum, simply divide by S
If it is NOT a regular polygon, that is, the internal angles are not all equal, you must have some sort of reference
Otherwise you will have to use a protractor and estimate.

Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
for regular polygons, the sum of the exterior angles is 360�

so, if n is the number of sides, one exterior angle is 360� divided by n

interior (inside) angles are supplementary to exterior angles (the pairs add to 180�)

so the value of an interior angle would be ___ 180 - (360 / n)

or ___ 180[(n - 2) / n]
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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:
http://www.mathopenref.com/polygoninteriorangles.html

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.

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