To determine the value of \( x \) given the angles 52°, 38°, 142°, and \( x \), we first need to know the context in which these angles are being used.
If they are to be summed up in some way (for instance, if they represent angles of a polygon), we need more information. In many cases, especially if we're dealing with a geometrical figure or a specific relationship (like supplementary or complementary angles), we need to work based on that context.
However, if we assume that the four angles must sum up to 360° (for instance, if they are angles around a point), we can set up the following equation:
\[ 52 + 38 + 142 + x = 360 \]
Calculating the sum of the known angles:
\[ 52 + 38 + 142 = 232 \]
Now, we can substitute this sum into the equation:
\[ 232 + x = 360 \]
To find \( x \), we subtract 232 from both sides:
\[ x = 360 - 232 \] \[ x = 128° \]
Thus, the value of \( x \) is:
\[ \boxed{128°} \]