SOLUTION: How do I find the value of x in the angles of a polygon?

Question 1052238: How do I find the value of x in the angles of a polygon?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have internal angles of a regular polygon and you have external angles of a regular polygon and you have central angles of a regular polygon.

the central angle of a polygon is equal to 360 / n, where n is the number of sides of the regular polygon.

the external angle of a polygon is equal to 360 / n, where n is the number of sides of the regular polygon.

the internal angle of a polygon is equal to the supplemental of the external angle of the polygon.

that makes the internal angle of a polygon equal to 180 minus the external angle of the regular polygon.

another formula for the internal angle of a regular polygon is:

x = 180 * (n-2) / n.

n is equal to the number of sides of the regular polygon.

here's some references:

http://www.regentsprep.org/regents/math/geometry/gg3/lpoly3.htm

http://www.regentsprep.org/regents/math/geometry/gg3/LPoly2.htm

http://www.mathopenref.com/polygoncentralangle.html

an example would be for the angles of an octagon (8 sided regular polygon).

each external angles is equal to 360/8 = 45 degrees.

each central angle is equal to 360/8 = 45 degrees - same as the external angle.

each interior angle is equal to 180 - 360/8 = 180 - 45 = 135 degrees.

each interior angle is also equal to 180 * (8 - 2) / 8 = 180 * 6 / 8 = 135 degrees.

the sum of the interior angles of the octagon is equal ti 8 * 135 = 1080 degrees.

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