Since triangles \( \triangle ABC \) and \( \triangle DEF \) are similar (denoted as \( \triangle ABC \sim \triangle DEF \)), the corresponding angles are equal. This means:
\[ m\angle A = m\angle D, \quad m\angle B = m\angle E, \quad m\angle C = m\angle F \]
From the information given, we have:
- \( m\angle A = 52^\circ \)
- \( m\angle E = 11^\circ \)
Since \( m\angle B = m\angle E \), we find that:
\[ m\angle B = 11^\circ \]
Now, we can find \( m\angle C \). The sum of angles in any triangle is \( 180^\circ \). Therefore,
\[ m\angle A + m\angle B + m\angle C = 180^\circ \]
Substituting the known values into the equation:
\[ 52^\circ + 11^\circ + m\angle C = 180^\circ \]
Calculating the current sum:
\[ 63^\circ + m\angle C = 180^\circ \]
Now, we can isolate \( m\angle C \):
\[ m\angle C = 180^\circ - 63^\circ \]
\[ m\angle C = 117^\circ \]
Thus, the measure of angle \( C \) is
\[ \boxed{117^\circ} \]