What is the measure of each exterior angle of a regular 2x gon?

A regular n-gon is a polygon with n equal sizes and n equal angles. 
A regular 3-gon is an equilateral triangle. 
A regular 4-gon is a square. 

Since all the angles of a regular polygon are equal, we don't have to measure each angle separately - measuring one measures them all. Furthermore, we know that a triangle's interior angles sum to 180, a rectangle's (since it contains 2 triangles) sum to 360, and in general an n-gon's (since it contains n-2 triangles) sum to 180*(n-2)=180n-360. There are n interior angles of equal measure, so each one has an equal share of this sum: each has measure 
(180n-360)/n. 

An exterior angle is found by extending one of the segments that meet at that angle beyond their intersection, and measuring the new angle formed there (not the interior angle that already existed, and not the 180-degree 'angle' that's on the other side which is just going from one side of that line to the other). 

Then the interior and exterior angles of a given vertex of a polygon sum to 180, so the exterior angle's measure is 180 minus the measure of the interior angle: in this case, 
180-(180n-360)/n = 180*(1-(n-2)/n) = 180*(n/n+(-n+2)/n) = 180*((n-n+2)/n) = 180*(2/n) =360/n. 

Then since the measure of the exterior angle of aregular n-gon is 360/n, and we're trying to find the measure of the exterior angle of a regular 2x-gon, plug 2x in for n: 
The measure of each exterior angle of a regular 2x-gon is 360/(2x), 
or 180/x. 

I hope that helps ^_^