MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

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°

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°