Question

Question Help Two angles are supplementary. One is 60° more than three times the other. Find the measures of the angles. (Supplementary angles are angles whose sum is 180°.) The measure of the smaller angle is (Simplify your answer.)

Answer 1

Let "x" be the smaller angle since the second angle is 60 more than three times this angle that means that if "y" is the second angle, then we have the following relationship:

`y=3x+60`

Since the sum of both angles must be 180 degrees, we have the following relationship:

`x+(3x+60)=180`

Now we solve for "x" first by adding like terms:

`4x+60=180`

Now we subtract 60 to both sides:

`\begin{gathered} 4x+60-60=180-60 \\ 4x=120 \end{gathered}`

Dividing by 4

`x=(120)/(4)=30`

Therefore, the smaller angle is 30 degrees.

The other angle is given by the relationship:

`y=3x+60`

We replace the value of "x":

`y=3(30)+60`

Solving the operations:

`y=90+60=150`

It can also be found knowin that the sum of both angle must be 180.