To find the value of \( x \), we need to use the definition of complementary angles: they sum up to 90°.
Given that one angle is 40° and the other angle is \( (8x + 2)° \), we can set up the equation:
\[ 40 + (8x + 2) = 90 \]
Now, simplify the equation:
\[ 40 + 8x + 2 = 90 \] \[ 8x + 42 = 90 \]
Next, subtract 42 from both sides:
\[ 8x = 90 - 42 \] \[ 8x = 48 \]
Now, divide by 8:
\[ x = \frac{48}{8} \] \[ x = 6 \]
Thus, the value of \( x \) is \( 6 \).