Prove that a regular 9-gon cannot be constructed by straightedge and compass.
Suppose to the contrary that we can construct a regular 9-gon. The internal angles of a 9-gon measure 140 degrees, so in particular a 140 degree angle is constructible. Given an angle, it is straightforward to construct its complement (simply extend one of the incident rays). So a 180-140 = 40 degree angle is also constructible, and bisecting, a 20 degree angle is constructible. However, as D&F argue on page 534, this is not possible. So a regular 9-gon cannot be constructed.