Respuesta :
Answer:
[tex]\begin{gathered} m\angle L=139^0 \\ m\angle S=41^0 \end{gathered}[/tex]Explanations:
If the sum of the measures of any two supplementary angles is 180 degrees and m[tex]m\angle L+m\angle S=180^0\text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1}[/tex]Also, if the measure of < L is sixty-six degrees less than five times the measure of < S, then:
[tex]m\angle L=5m\angle S-66_{--------------}2[/tex]Substitute equation 2 into equation 1 to have:
[tex](5m\angle S-66)+m\angle S=180[/tex]Simplify the result to have:
[tex]\begin{gathered} 5m\angle S-66+m\angle S=180 \\ 5m\angle S+m\angle S-66=180 \\ 6m\angle S-66=180 \end{gathered}[/tex]Add 66 to both sides of the resulting equation:
[tex]\begin{gathered} 6m\angle S-66+66=180+66 \\ 6m\angle S=246 \end{gathered}[/tex]Divide both sides of the equation by 6
[tex]\begin{gathered} \frac{\cancel{6}m\angle S}{\cancel{6}}=\frac{\cancel{246}^{41}}{\cancel{6}} \\ m\angle S=41^0 \end{gathered}[/tex]Get the measure of < L. Recall that:
[tex]\begin{gathered} m\angle L=5m\angle S-66 \\ m\angle L=5(41)-66 \\ m\angle L=205-66 \\ m\angle L=139^0 \end{gathered}[/tex]Hence the measure of < L is 139 deg. while the measure of
