## Intermediate Algebra (12th Edition)

$(3x+5)^o=65^o ,\\ (5x+15)^o=115^o$
$\bf{\text{Solution Outline:}}$ Equate the given supplementary angles to $180$, and use the properties of equality to isolate $x.$ Then substitute the value of $x$ in the following given supplementary angles: \begin{array}{l}\require{cancel} (3x+5)^o ,\\ (5x+15)^o .\end{array} $\bf{\text{Solution Details:}}$ Since the sum of supplementary angles is $180^o,$ then \begin{array}{l}\require{cancel} (3x+5)+(5x+15)=180 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 3x+5x=180-5-15 \\\\ 8x=160 \\\\ x=\dfrac{160}{8} \\\\ x=20 .\end{array} Substituting $x= 20$ in the angle $(3x+5)^o$ results to \begin{array}{l}\require{cancel} (3\cdot20+5)^o \\\\= (60+5)^o \\\\= 65^o .\end{array} Substituting $x= 20$ in the angle $(5x+15)^o$ results to \begin{array}{l}\require{cancel} (5\cdot20+15)^o \\\\= (100+15)^o \\\\= 115^o .\end{array} Hence, the measures of the complementary angles are \begin{array}{l}\require{cancel} (3x+5)^o=65^o ,\\ (5x+15)^o=115^o .\end{array}