If all of the angles of a hexagon are congruent, then what is the measure of each angle?

he total number of internal degrees is (n-2)*180 = 4*180 = 720 degrees.

let a = one of the congruent angles.
you have:
angles 1, 2, and 3 = a.

if a = 2 * angle 4, then angle 4 = 1/2 * a

if a = 1/2 * angle 5, then angle 5 = 2 * a

we have:
angle 1 = a
angle 2 = a
angle 3 = a
angle 4 = 1/2 * a
angle 5 = 2 * a
angle 6 = 115

since the sum of the angles is equal to 720, we have:
3*a + 2*a + 1/2*a + 115 = 720
combine like terms to get:
5.5 * a + 115 = 720
subtract 115 from both sides to get:
5.5 * a = 720 - 115 = 605
divide both sides by 5.5 to get:
a = 720/5.5 = 110

angle 1, 2, and 3 are each 110 degrees.
angle 4 = 55 degrees
angle 5 = 220 degrees
angle 6 = 115 degrees

the question is:
What is the measure of the smallest angle?
the answer is:
55 degrees.

It should be 120° 
Someone else correct me if I'm wrong.

Hope this helps!