Since triangle ABC is similar to triangle DEF (denoted as \( \triangle ABC \sim \triangle DEF \)), corresponding angles are equal. This means that the measures of angles in triangle ABC correspond to the measures of angles in triangle DEF in the same order.
Given:
- \( m\angle A \) (the measure of angle A in triangle ABC) is provided in degrees.
- \( m\angle E = 11 \) degrees (the measure of angle E in triangle DEF).
Since the angles are corresponding: \[ m\angle A = m\angle D \] \[ m\angle B = m\angle E \] \[ m\angle C = m\angle F \]
From the information given, we note \( m\angle E = 11\) degrees. Therefore, since \( m\angle B \) corresponds to \( m\angle E \): \[ m\angle B = 11 \text{ degrees} \]
Now, we know that the sum of the angles in a triangle is \( 180 \) degrees. Thus, for triangle ABC, we can express the sum of the angles as: \[ m\angle A + m\angle B + m\angle C = 180 \text{ degrees} \]
Substituting \( m\angle B \) into the equation gives: \[ m\angle A + 11 + m\angle C = 180 \]
Rearranging it we find: \[ m\angle C = 180 - m\angle A - 11 \] \[ m\angle C = 169 - m\angle A \]
To find the exact measure of angle \( C \), we need the specific measure of angle \( A \). If you provide that value, we can calculate it directly!