The measures of two supplementary angles have a ratio of 2: 4. what is the measure of the smaller angle

Comment
The way to handle this is to realize that the 180 degree angle (the two supplementary angles added together to make 180o by definition) is actually divided into 6 parts. There are 2 parts for the smaller angle and 4 for the larger.

Added together the 2 angles = 180

Equation
Let one of the 6 parts = x
2x + 4 x = 180

Solve
2x + 4x = 180 Add the like terms on the left together.
6x = 180  Divide by 6
x = 180/6
x = 30

Answer
Since one angle is 2 parts (the smaller angle)
2 * 30 = 60
And the larger angle is
4 * 30 = 120 

The two angles are
60,120 <<<< answer.

Further comment.
The two angles are supplementary 60 + 120 = 180
One angle is twice as big as the other. 2*60 = 120

Two supplementary angles have a ratio of 2:4 (or 1:2) reduced

supplementary angle = 180°

s = a angle (2), as 2s = (4) in the ratio

s + 2s = 180

3s = 180

isolate the s

3s/3 = 180/3

s = 180/3

s  = 60

2s = 2(60) = 120

The measurement of the smaller angle is 60°, while the larger is 120°

hope this helps