The larger of two supplementary angles measures 20° less than four times the measures of the smaller angle .find the degree measure of each angle

Supplementary angles by definition means the sum is 180.
From that knowledge we can write up some equations.
Let angle 1 = x, and angle 2 = y

x + y = 180

"The larger of two supplementary angles measures 20° less than four times the measure of the smaller angle"
(Let x be the larger angle)
x+20 = 4y

Since there are two different equations, and two variables, this means we have a set of simultaneous equations.
We can solve this via the substitution method or the elimination method.

I choose to solve it via the substitution method cause of personal preference.
x + y = 180  =>  x = 180- y
x+20 = 4y => x = 4y - 20
Make them equal each other..
180 - y = 4y - 20
200 = 5y
40 = y
Now that we know y we can sub it into any equation to find x
x + 20 = 4y
x + 20 = 4(40)
x + 20 = 160
x = 140
So the angles are 40° and 140°