Supplementary angles are two angles that add up to 180 degrees. If \( m∠k = 117° \), you can find \( m∠j \) using the following formula:
\[ m∠j + m∠k = 180° \]
Substituting the value of \( m∠k \):
\[ m∠j + 117° = 180° \]
To find \( m∠j \), subtract 117° from both sides:
\[ m∠j = 180° - 117° = 63° \]
So, \( m∠j = 63° \).