Two angles are considered complementary if their measures add up to 90 degrees. In this case, we have the two angles as \( (2x)^\circ \) and \( (3x)^\circ \).
We can set up the equation:
\[ (2x) + (3x) = 90 \]
Combining the terms, we get:
\[ 5x = 90 \]
Now, we can 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:
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For the angle \( (2x)^\circ \): \[ 2x = 2(18) = 36^\circ \]
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For the angle \( (3x)^\circ \): \[ 3x = 3(18) = 54^\circ \]
Therefore, the results are:
- \( x = 18 \)
- \( (2x)^\circ = 36^\circ \)
- \( (3x)^\circ = 54^\circ \)
So the final answer is: \( x = 18 \), \( (2x)^\circ = 36^\circ \), and \( (3x)^\circ = 54^\circ \).