Answer :
Let the measure of ∠L be x, and let the measure of ∠S be y.
Since it is given that they are supplementary, that is, the sum of their measures is 180⁰, it follows that:
[tex]x+y=180[/tex]It is also given that the measure of ∠L is 36⁰ less than three times the measure of ∠S. Hence, the equation is:
[tex]x=3y-36[/tex]The resulting system of equations to be solved is:
[tex]\begin{cases}x+y=180 \\ x=3y-36\end{cases}[/tex]Solve the resulting system of equations.
Substitute the expression for x in the second equation into the first equation:
[tex](3y-36)+y=180[/tex]Solve the equation for y:
[tex]\begin{gathered} 3y-36+y=180 \\ \text{collect like terms:} \\ \Rightarrow3y+y=180+36 \\ \Rightarrow4y=216 \\ \Rightarrow\frac{4y}{4}=\frac{216}{4} \\ \Rightarrow y=54 \end{gathered}[/tex]Substitute y=54 into the second equation:
[tex]x=3(54)-36=162-36=126[/tex]It follows that the measure of ∠L is 126⁰ and the measure of ∠S is 54⁰.
(Remember to use 'deg' for the degree symbol as instructed).