Complementary angles are two angles that add up to \(90^\circ\). Given the measures of the angles as \( (2x)^\circ \) and \( (3x)^\circ \), we can set up the equation:
\[ 2x + 3x = 90 \]
Combining like terms gives:
\[ 5x = 90 \]
Now, solving for \(x\):
\[ x = \frac{90}{5} = 18 \]
Now we can find the measures of the two angles:
- For \( (2x)^\circ \):
\[ (2x)^\circ = 2(18)^\circ = 36^\circ \]
- For \( (3x)^\circ \):
\[ (3x)^\circ = 3(18)^\circ = 54^\circ \]
So, the values are:
\[ x = 18, \quad (2x)^\circ = 36^\circ, \quad (3x)^\circ = 54^\circ \]
Final answer: \( x = 18, (2x)^\circ = 36^\circ, (3x)^\circ = 54^\circ \)