Two complementary angles have measures in the ration 1:2. what is the measure of the smaller angle?

Complementary angles add up to 90 degrees. So say that the two angles you have are x and y. If the angles are in a 1:2 ratio, you are basically splitting them up into 3 groups. So splitting the 90 degrees into 3 groups gets 30 degrees into each group. You only care about the smaller angle, which makes up one group, so the smaller angle is 30 degrees.