Two angles are supplementary if the sum of their measures is \(180^\circ\).
Given that \(m∠k = 117^\circ\), we can find \(m∠j\) using the following equation:
\[ m∠j + m∠k = 180^\circ \]
Substituting the value of \(m∠k\):
\[ m∠j + 117^\circ = 180^\circ \]
Now, to find \(m∠j\), subtract \(117^\circ\) from \(180^\circ\):
\[ m∠j = 180^\circ - 117^\circ = 63^\circ \]
Thus, \(m∠j = 63^\circ\).