Question

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

Answer 1

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°