Question 1052238
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:


<a href = "http://www.regentsprep.org/regents/math/geometry/gg3/lpoly3.htm" target = "_blank">http://www.regentsprep.org/regents/math/geometry/gg3/lpoly3.htm</a>


<a href = "http://www.regentsprep.org/regents/math/geometry/gg3/LPoly2.htm" target = "_blank">http://www.regentsprep.org/regents/math/geometry/gg3/LPoly2.htm</a>


<a href = "http://www.mathopenref.com/polygoncentralangle.html" target = "_blank">http://www.mathopenref.com/polygoncentralangle.html</a>


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.