Supplementary angles are two angles whose measures add up to 180 degrees.
Given that \( m<k = 117^\circ \), we can find \( m<j \) using the equation:
\[ m<j + m<k = 180^\circ \]
Substituting the value of \( m<k \):
\[ m<j + 117^\circ = 180^\circ \]
Now, subtract 117 degrees from both sides:
\[ m<j = 180^\circ - 117^\circ \]
\[ m<j = 63^\circ \]
So, \( m<j = 63^\circ \).