#### Answer

$(3x-9)^o=24^o
,\\
(6x)^o=66^o$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Equate the given complementary angles to $90$, and use the properties of equality to isolate $x.$ Then substitute the value of $x$ in the following given complementary angles:
\begin{array}{l}\require{cancel}
(3x-9)^o
,\\
(6x)^o
.\end{array}
$\bf{\text{Solution Details:}}$
Since the sum of complementary angles is $90^o,$ then
\begin{array}{l}\require{cancel}
(3x-9)+(6x)=90
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
3x+6x=90+9
\\\\
9x=99
\\\\
x=\dfrac{99}{9}
\\\\
x=11
.\end{array}
Substituting $x=
11
$ in the angle $
(3x-9)^o
$ results to
\begin{array}{l}\require{cancel}
(3\cdot11-9)^o
\\\\=
(33-9)^o
\\\\=
24^o
.\end{array}
Substituting $x=
11
$ in the angle $
(6x)^o
$ results to
\begin{array}{l}\require{cancel}
(6\cdot11)^o
\\\\=
66^o
.\end{array}
Hence, the measures of the complementary angles are
\begin{array}{l}\require{cancel}
(3x-9)^o=24^o
,\\
(6x)^o=66^o
.\end{array}