Complementary angles are two angles whose measures add up to \(90^\circ\). We are given one angle measuring \(36^\circ\) and the other angle measuring \((x - 3)^\circ\). We can set up the following equation to represent the relationship between these two angles:
\[ 36 + (x - 3) = 90 \]
Now, let's simplify and solve for \(x\):
\[ 36 + x - 3 = 90 \] \[ x + 33 = 90 \] \[ x = 90 - 33 \] \[ x = 57 \]
Now that we know \(x = 57\), we can find the measure of the unknown angle:
\[ x - 3 = 57 - 3 = 54 \]
Thus, the value of \(x\) is \(57\) and the measure of the unknown angle is \(54^\circ\).