Question

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Two angles are supplementary. The measure of the larger angle is 5 more than 4 times the measure of the smaller angle. Find the measure of both angles.

Answer 1

Explanation:

Call the larger angle x and the smaller angle y. The fact that the angles are supplementary means that they add to 180 degrees. We could write:

x+y=180

We are also told that the measure of the larger angle is 5 more than 4 times the measure of the smaller angle, which we could write as:

x=4y+5

We have a system of two equations, which we can solve for x and y. Substitute the second into the first and solve for y.

(4+5)+y=180

5y+5=180

5y=175

y=35

Now substitute y into the first equation and solve for x.

x+35=180

x=145

x=145, y=35.

Answer 2

4x+5 (angle 1)
x (angle 2)

4x+5+x=180
5x=175
x=35

4x+5
=4(35)+5
=145

This means the small angle is 35 degrees and the big angle is 145 degrees.