To find the value of \( n \) such that \( (12n)^\circ \) and \( 132^\circ \) are equal, we can set up the equation:
\[ 12n = 132 \]
Now, we solve for \( n \):
\[ n = \frac{132}{12} \]
Calculating the right side:
\[ n = 11 \]
Thus, the value of \( n \) is
\[ \boxed{11} \]