Question

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

Answer 1

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

Answer 2

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