Respuesta :

nathan127
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°
facundo3141592

We want to create a system of equations that allows us to find the values of two supplementary angles.

We will find that the larger angle measures 140° and the smaller one measures 40°.

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Two angles A and B are supplementary if their measures add up to 180°, so we have:

A + B = 180°.

Let's assume that B is the larger one, we also do know that:

"The larger is 20° less than 4 times the smaller"

Then we can write:

B = 4*A - 20°.

Then our system of equations is:

A + B = 180°.

B = 4*A - 20°.

To solve it we need to isolate one variable in one of the equations and replace it on the other equation. Here we can see that B is already isolated on the second equation, so we can replace it in the first one to get:

A + B = 180°.

A + (4*A - 20°) = 180°

Now we can solve this for A:

A + (4*A - 20°) = 180°

5*A - 20° = 180°

5*A = 180° + 20° = 200°

A = 200°/5 = 40°

Now that we know the value of A we can get the value of B:

B = 4*A - 20° = 4*40° - 20° = 140°

Then the larger angle measures 140° and the smaller measures 40°

If you want to learn more, you can read:

https://brainly.com/question/18164299

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