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