To find the value of \( x \), we need to utilize the fact that the two adjacent angles are inside a 90° angle. This means that the sum of the two angles must be equal to 90°.
Given:
- The first angle measures \( (x + 4)^\circ \)
- The second angle measures \( (3x + 2)^\circ \)
We can set up the equation:
\[ (x + 4) + (3x + 2) = 90 \]
Now, let's simplify and solve for \( x \):
\[ x + 4 + 3x + 2 = 90 \]
Combine like terms:
\[ 4x + 6 = 90 \]
Next, subtract 6 from both sides:
\[ 4x = 90 - 6 \] \[ 4x = 84 \]
Now, divide both sides by 4:
\[ x = \frac{84}{4} = 21 \]
Thus, the value of \( x \) is \( \boxed{21} \).