Since triangles \( \triangle ABC \) and \( \triangle DEF \) are similar, their corresponding angles are equal. This means:
\[ m\angle A = m\angle D, \] \[ m\angle B = m\angle E, \] \[ m\angle C = m\angle F. \]
We know that:
\[ m\angle A = 52^\circ, \] \[ m\angle E = 11^\circ. \]
To find \( m\angle B \):
\[ m\angle B = m\angle E = 11^\circ. \]
Now, we can find \( m\angle C \). The sum of the angles in a triangle is \( 180^\circ \). Therefore, for triangle \( ABC \):
\[ m\angle A + m\angle B + m\angle C = 180^\circ. \]
Substituting the known values:
\[ 52^\circ + 11^\circ + m\angle C = 180^\circ. \]
Adding the angles we have:
\[ 63^\circ + m\angle C = 180^\circ. \]
Now, we can solve for \( m\angle C \):
\[ m\angle C = 180^\circ - 63^\circ = 117^\circ. \]
Thus, the measure of angle \( C \) is
\[ \boxed{117^\circ}. \]