#### Answer

$(9-5x)^o=49^o
,\\
(25-3x)^o=49^o$

#### 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}
(9-5x)^o
,\\
(25-3x)^o
.\end{array}
$\bf{\text{Solution Details:}}$
Since vertical angles have the same measure, then
\begin{array}{l}\require{cancel}
9-5x=25-3x
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
-5x+3x=25-9
\\\\
-2x=16
\\\\
x=\dfrac{16}{-2}
\\\\
x=-8
.\end{array}
Substituting $x=
-8
$ in the angle $
(9-5x)^o
$ results to
\begin{array}{l}\require{cancel}
(9-5\cdot(-8))^o
\\\\=
(9+40)^o
\\\\=
49^o
.\end{array}
Substituting $x=
-8
$ in the angle $
(25-3x)^o
$ results to
\begin{array}{l}\require{cancel}
(25-3\cdot(-8))^o
\\\\=
(25+24)^o
\\\\=
49^o
.\end{array}
Hence, the measures of the vertical angles are
\begin{array}{l}\require{cancel}
(9-5x)^o=49^o
,\\
(25-3x)^o=49^o
.\end{array}