Supplementary angles are angles that add up to 180 degrees. If \( m \angle j = 34^\circ \), you can find \( m \angle k \) by using the equation:
\[ m \angle j + m \angle k = 180^\circ \]
Substituting the value of \( m \angle j \):
\[ 34^\circ + m \angle k = 180^\circ \]
To solve for \( m \angle k \), subtract \( 34^\circ \) from \( 180^\circ \):
\[ m \angle k = 180^\circ - 34^\circ = 146^\circ \]
Therefore, \( m \angle k = 146^\circ \).