Complementary angles are two angles that add up to 90 degrees. Given that the measures of the two angles are \( (2x)^\circ \) and \( (3x)^\circ \), we can set up the equation:
\[ 2x + 3x = 90 \]
This simplifies to:
\[ 5x = 90 \]
To find the value of \( x \), divide both sides by 5:
\[ x = \frac{90}{5} = 18 \]
Now we can find the measures of the two angles:
- For the first angle \( (2x)^\circ \):
\[ 2x = 2(18) = 36^\circ \]
- For the second angle \( (3x)^\circ \):
\[ 3x = 3(18) = 54^\circ \]
Now we have the values:
- \( x = 18 \)
- \( (2x)^\circ = 36^\circ \)
- \( (3x)^\circ = 54^\circ \)
Thus, the final answers are:
\[ x = 18, \quad (2x)^\circ = 36^\circ, \quad (3x)^\circ = 54^\circ \]