To find the measure of the reflex angle \( g \), we need to understand that a reflex angle is an angle that is greater than \( 180^\circ \) but less than \( 360^\circ \).
Given that one angle measures \( 70^\circ \), the reflex angle \( g \) can be calculated by subtracting the smaller angle from \( 360^\circ \):
\[ g = 360^\circ - 70^\circ \]
Calculating that gives:
\[ g = 290^\circ \]
Thus, the measure of the reflex angle \( g \) is \( 290^\circ \).