Question

The sum of the measures of any two supplementary angles is 180°. ZL and ZS aresupplementary angles. The measure of 2L is thirty-six degrees less than three timesthe measure of ZS.What is the measure of L? Use "deg" for the degree symbol.What is the measure of S? Use "deg" for the degree symbol.Please see the picture

Answer 1

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:

`x+y=180`

It is also given that the measure of ∠L is 36⁰ less than three times the measure of ∠S. Hence, the equation is:

`x=3y-36`

The resulting system of equations to be solved is:

`\begin{cases}x+y=180 \\ x=3y-36\end{cases}`

Solve the resulting system of equations.

Substitute the expression for x in the second equation into the first equation:

`(3y-36)+y=180`

Solve the equation for y:

`\begin{gathered} 3y-36+y=180 \\ \text{collect like terms:} \\ \Rightarrow3y+y=180+36 \\ \Rightarrow4y=216 \\ \Rightarrow(4y)/(4)=(216)/(4) \\ \Rightarrow y=54 \end{gathered}`

Substitute y=54 into the second equation:

`x=3(54)-36=162-36=126`

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).