Question

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 1

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:

`A=8+3B`

As they are supplementary, they add 180 degrees:

`A+B=180`

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

`\begin{gathered} A=180-B \\ A=8+3B=180-B \\ 8+3B=180-B \\ 4B+B=180-8 \\ 5B=172 \\ B=(172)/(5) \\ B=34.4 \end{gathered}`

Now we can solve for the other angle:

`A=8+3B=8+3(34.4)=8+103.2=111.2`

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