Using a compass and a straightedge only, it is not possible to contruct an angle with measure equal to ___the measure of a given angle.
a. 1/2
b. 1/4
c. 1/6
d. 3/8

Question

Using a compass and a straightedge only, it is not possible to contruct an angle with measure equal to ___the measure of a given angle. 
a. 1/2
b. 1/4
c. 1/6
d. 3/8

anonymous · Answer

Note that all the denominators are powers of of two except one.  We can bisect to get half angles, bisect again to get quarter angles, and again to get eighths.  There is no way to break an angle into thirds with just a straightedge and compass, hence sixths are not possible either.