**Solution**

Let the measure of the required angle be $x^{\circ}$.

Then, measure of its supplement $=(180-x)^{\circ}$.

$$

\therefore \quad(180-x)-x=32 \Rightarrow 2 x=148 \Rightarrow x=74 \text {. }

$$

Hence, the measure of the required angle is $74^{\circ}$.