Two angles are supplementary if their sum is​ 180°. the larger angle measures five degrees more than four times the measure of a smaller angle. if x represents the measure of the smaller angle and these two angles are​ supplementary, find the measure of each angle.

Let x represent the smaller angle.
Let y represent the larger angle.

The problem states that the larger angle measures five degrees more than four times the measure of the smaller angle.
With this given information, we can create the following equation.

[tex]y=4x+5[/tex]

Also, they a supplementary, meaning that they add up to 180. We can create another equation.

[tex]x+y=180[/tex]

Since we have two linear equations and we want to find the solution, we have a system of linear equations. Let's solve this system by using the substitution method.

Substitute [tex]y=4x+5[/tex] into [tex]x+y=180[/tex]

[tex]x+y=180[/tex]

After substituting, you get

[tex]x+4x+5=180[/tex]

Now, combine the x's

[tex]5x+5=180[/tex]

Subtract both sides by 5

[tex]5x=175[/tex]

Divide both sides by 5.

[tex]x=35[/tex]

Now, we can solve for y using the equation [tex]x+y=180[/tex] since we know the value of x.

[tex]35+y=180[/tex]

Subtract both sides by 35.

[tex]y=145[/tex]

The smaller angle has a measure of 35 degrees and the larger one has a measure of 145 degrees. Have an awesome day! :)