To find the measure of the exterior angle \( x \) of a triangle, we can use the fact that the exterior angle is equal to the sum of the two opposite interior angles.
Let's denote the interior angles of the triangle as follows:
- Angle A: 35 degrees
- Angle B: 42 degrees
- Angle C: \( C \)
The sum of the angles in a triangle is 180 degrees, so we can find angle C:
\[ C = 180 - (A + B) = 180 - (35 + 42) = 180 - 77 = 103 \text{ degrees} \]
Now, the exterior angle \( x \) corresponding to angle C can be calculated as follows:
\[ x = A + B = 35 + 42 = 77 \text{ degrees} \]
Thus, the measure of the exterior angle \( x \) is:
\[ \boxed{77 \text{ degrees}} \]