To find the measure of the exterior angle \( X \), we can use the fact that the exterior angle of a polygon is equal to the sum of the two remote interior angles. However, since you only provided two angles \( 39^\circ \) and \( 43^\circ \), it is unclear whether these represent interior angles of a triangle or some other polygon.
If we assume that \( 39^\circ \) and \( 43^\circ \) are the two interior angles of a triangle, we can find the third interior angle using the fact that the sum of angles in a triangle is \( 180^\circ \):
\[ \text{Third angle} = 180^\circ - (39^\circ + 43^\circ) = 180^\circ - 82^\circ = 98^\circ \]
According to the exterior angle theorem, the exterior angle \( X \) at any vertex of a triangle is equal to the sum of the two remote interior angles. So, if we are finding the exterior angle at the angle \( 98^\circ \):
\[ X = 39^\circ + 43^\circ = 82^\circ \]
Thus, the measure of the exterior angle \( X \) is \( 82^\circ \).