To find the measure of the exterior angle \( x \) in a triangle where the interior angles are 74 degrees and 53 degrees, we can use the fact that the sum of the interior angles of a triangle is equal to 180 degrees.
First, let's find the third interior angle:
\[ \text{Third angle} = 180^\circ - (74^\circ + 53^\circ) \]
Calculating the sum of the two given angles:
\[ 74^\circ + 53^\circ = 127^\circ \]
Now, the third angle is:
\[ \text{Third angle} = 180^\circ - 127^\circ = 53^\circ \]
Now, to find the exterior angle \( x \), we can use the fact that the exterior angle is equal to the sum of the two non-adjacent interior angles (in this case, any of the other two angles):
\[ x = 74^\circ + 53^\circ \]
Calculating this:
\[ x = 74^\circ + 53^\circ = 127^\circ \]
Therefore, the measure of the exterior angle \( x \) is:
\[ \boxed{127} \text{ degrees} \]