To find the value of \( x \), we start with the definition of complementary angles. Two angles are complementary if the sum of their measures equals \( 90^\circ \).
Given:
- One angle is \( 40^\circ \).
- The other angle is \( (8x + 2)^\circ \).
Setting up the equation, we have: \[ 40 + (8x + 2) = 90 \]
Now, simplify the equation: \[ 40 + 8x + 2 = 90 \] \[ 8x + 42 = 90 \]
Next, isolate \( 8x \): \[ 8x = 90 - 42 \] \[ 8x = 48 \]
Now, divide both sides by 8: \[ x = \frac{48}{8} \] \[ x = 6 \]
Thus, the value of \( x \) is \( 6 \).
The correct answer is C. 6.