Since triangles \( \Delta ABC \) and \( \Delta DEF \) are similar (denoted as \( \Delta ABC \sim \Delta DEF \)), the corresponding angles of the triangles are equal.
According to the property of similar triangles:
- \( m \angle A \) corresponds to \( m \angle D \)
- \( m \angle B \) corresponds to \( m \angle E \)
- \( m \angle C \) corresponds to \( m \angle F \)
Based on the provided information:
- \( m \angle A = 52^\circ \)
- \( m \angle E = 11^\circ \)
To find \( m \angle C \):
-
First, we can find \( m \angle B \) (since \( m \angle B \) corresponds to \( m \angle E \)): \[ m \angle B = m \angle E = 11^\circ \]
-
The sum of the angles in any triangle is \( 180^\circ \): \[ m \angle A + m \angle B + m \angle C = 180^\circ \]
-
Substitute the known values: \[ 52^\circ + 11^\circ + m \angle C = 180^\circ \]
-
Combine the known angles: \[ 63^\circ + m \angle C = 180^\circ \]
-
Solve for \( m \angle C \): \[ m \angle C = 180^\circ - 63^\circ = 117^\circ \]
Thus, the measurement of angle \( C \) is \( \boxed{117^\circ} \).