To find the measure of \( x \) for the two adjacent angles \( x^\circ \) and \( (x + 30)^\circ \), which together sum to \( 90^\circ \), we can set up the following equation:
\[ x + (x + 30) = 90 \]
Combining like terms, we have:
\[ 2x + 30 = 90 \]
Next, we can subtract \( 30 \) from both sides:
\[ 2x = 90 - 30 \] \[ 2x = 60 \]
Now, we divide by \( 2 \):
\[ x = \frac{60}{2} \] \[ x = 30 \]
Thus, the value of \( x \) is 30.