To find the measure of the reflex angle \( j \) when given that one angle is \( 120^\circ \), we can use the following relationship:
A full circle is \( 360^\circ \). A reflex angle is the angle that is greater than \( 180^\circ \) and less than \( 360^\circ \).
The reflex angle \( j \) can be calculated as follows:
\[ j = 360^\circ - 120^\circ \]
Calculating this:
\[ j = 360^\circ - 120^\circ = 240^\circ \]
Thus, the measure of the reflex angle \( j \) is \( 240^\circ \).