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4) The measure of one of two supplementary angles is 8 degrees more than three times the other. Find the measure of the larger of the two angles.

Answer :

Supplementary angles add 180 degrees.

One of the two angles is 8 degrees more than 3 times the other.

If one of the angles is A and the other is B, then:

[tex]A=8+3B[/tex]

As they are supplementary, they add 180 degrees:

[tex]A+B=180[/tex]

We replace the information of the second equation in the first one and solve:

[tex]\begin{gathered} A=180-B \\ A=8+3B=180-B \\ 8+3B=180-B \\ 4B+B=180-8 \\ 5B=172 \\ B=\frac{172}{5} \\ B=34.4 \end{gathered}[/tex]

Now we can solve for the other angle:

[tex]A=8+3B=8+3(34.4)=8+103.2=111.2[/tex]

The measure of the angles is 34.4 degrees and 111.2 degrees.

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