Question

Two angles are supplementary angles if the sum of their measures is 180. Find the measures of two supplementary angles if the measure of one angle is 4 degrees less than three times the other.What are the measures of the two angles?

Answer 1

The measures of the two angles are 46° and 134°.

Step-by-step explanation:

Let x and y be the two angles:

x+y=180

It is mentioned that the measure of one angle is 4 degrees less than three times the other.

Let:

y=3x-4

Then, we substitute y=3x-4 into x+y=180.

So,

`\begin{gathered} x+y=180 \\ x+(3x-4)=180 \\ \text{Simplify and rearrange} \\ x+3x-4=180 \\ 4x=180+4 \\ 4x=184 \\ x=(184)/(4) \\ \text{Calculate} \\ x=46 \end{gathered}`

We substitute x=46 into x+y=180. So,

`\begin{gathered} x+y=180 \\ 46+y=180 \\ \text{Simplify and rearrange} \\ y=180-46 \\ \text{Calculate} \\ y=134 \end{gathered}`

Therefore, the measures of the two angles are 46° and 134°.