Supplementary angles are two angles that add up to 180 degrees.
Given that the measure of angle \( k \) is \( 117^\circ \), we can find the measure of angle \( j \) as follows:
\[ \text{Measure of } \angle j = 180^\circ - \text{Measure of } \angle k \]
\[ \text{Measure of } \angle j = 180^\circ - 117^\circ = 63^\circ \]
Therefore, the measure of angle \( j \) is \( 63^\circ \).
The answer is 63°.