Answer
$(3x+5)^o=65^o
,\\
(5x+15)^o=115^o$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
