In a pair of complementary angles, the sum of their measures is \(90^\circ\).
Given that one angle measures \(36^\circ\) and the other measures \((x - 3)^\circ\), we can set up the equation:
\[ 36 + (x - 3) = 90 \]
Now, simplify the equation:
\[ 36 + x - 3 = 90 \]
Combine like terms:
\[ x + 33 = 90 \]
Now, isolate \(x\) by subtracting \(33\) from both sides:
\[ x = 90 - 33 \] \[ x = 57 \]
Now, we need to find the measure of the unknown angle, \((x - 3)\):
\[ x - 3 = 57 - 3 = 54 \]
Thus, the solutions are:
\[ x = 57, \quad \text{unknown angle measure} = 54^\circ \]
So the final answers are:
\(x = 57\), \( \text{unknown angle measure} = 54^\circ\).