Given the information that angles \( A \) and \( B \) are vertical angles, we know that vertical angles are equal. Therefore:
\[ m\angle B = m\angle A = 22^\circ \]
Since angle \( B \) is complementary to angle \( C \), we know that the sum of the measures of these two angles is \( 90^\circ \):
\[ m\angle B + m\angle C = 90^\circ \]
Now, substituting the measure of angle \( B \):
\[ 22^\circ + m\angle C = 90^\circ \]
To solve for \( m\angle C \), we can rearrange the equation:
\[ m\angle C = 90^\circ - 22^\circ \]
Thus, you can use the following equation to solve for \( m\angle C \):
\[ m\angle C = 90^\circ - m\angle B \]
or specifically with the known value:
\[ m\angle C = 90^\circ - 22^\circ \]