#### Answer

$(7x+17)^o=122^o
,\\
(8x+2)^o=122^o$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Equate the given vertical angles, and use the properties of equality to isolate $x.$ Then substitute the value of $x$ in the following given vertical angles:
\begin{array}{l}\require{cancel}
(7x+17)^o
,\\
(8x+2)^o
.\end{array}
$\bf{\text{Solution Details:}}$
Since vertical angles have the same measure, then
\begin{array}{l}\require{cancel}
7x+17=8x+2
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
7x-8x=2-17
\\\\
-x=-15
\\\\
x=15
.\end{array}
Substituting $x=
15
$ in the angle $
(7x+17)^o
$ results to
\begin{array}{l}\require{cancel}
(7\cdot15+17)^o
\\\\=
(105+17)^o
\\\\=
122^o
.\end{array}
Substituting $x=
15
$ in the angle $
(8x+2)^o
$ results to
\begin{array}{l}\require{cancel}
(8\cdot15+2)^o
\\\\=
(120+2)^o
\\\\=
122^o
.\end{array}
Hence, the measures of the vertical angles are
\begin{array}{l}\require{cancel}
(7x+17)^o=122^o
,\\
(8x+2)^o=122^o
.\end{array}