Question

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

Answer 1

Simplify 2:4
you get 1:2

this means the larger is two times the smaller.

well, we have to use a system of equations.

we know two supplementary angles add up to be 180°.we can create our first equaition, using 

smaller angle + larger angle = 180
s + l = 180

we can create our second equation using 
two times the smaller = larger
2s = l

our two equations are:
2s = l
s + l = 180

now that we have  the two equations, we can solve using subsitution to isolate the variable.
s + l = 180
s + (2s) = 180

simpify.

3s = 180
s = 60

the smaller angle has a value of 60.
now, remember that the larger angle is two times the smaller.

60 x 2 = 120

smaller angle: 60
larger angle: 120

we know this is correct because we know the smaller is 1/2 or 1:2 or 2:4 times the bigger, and the two angles add up to be 180 (60 + 120)

hope this helps and have a great day!