Question

The measures of exterior angles of a regular polygon with n numbers of sides ______ as n increases.

increases
decreases
remains the same

Answer 1

The total of the degrees of the exterior angles has to be 360 degrees, so the more sides you have, the smaller each angle has to be for them to still add to 360 deg.

So, for a square (n=4), 4a = 360
a = 90 degrees

For n = 5, 5a = 360, so a = 72 degrees
etc.

Here is a cool picture about the exterior angles of polygons: http://www.mathsisfun.com/geometry/exterior-angles-polygons.html

Answer 2

So to answer the question: "decreases"