Supplementary angles are two angles whose measures add up to \(180^\circ\).
Given that \(m\angle j = 34^\circ\), we can find \(m\angle k\) using the formula for supplementary angles:
\[ m\angle j + m\angle k = 180^\circ \]
Substituting the value of \(m\angle j\):
\[ 34^\circ + m\angle k = 180^\circ \]
To find \(m\angle k\), subtract \(34^\circ\) from \(180^\circ\):
\[ m\angle k = 180^\circ - 34^\circ = 146^\circ \]
Thus, \(m\angle k = 146^\circ\).