Complementary angles are two angles that add up to 90 degrees. Given the measures of the two angles as (2x)° and (3x)°, we can write the equation:
\[ 2x + 3x = 90 \]
Combining the terms gives us:
\[ 5x = 90 \]
Next, we can solve for \(x\) by dividing both sides by 5:
\[ x = \frac{90}{5} = 18 \]
Now we can find the measures of the two angles:
- For the angle measuring \(2x\):
\[ 2x = 2(18) = 36° \]
- For the angle measuring \(3x\):
\[ 3x = 3(18) = 54° \]
Thus, the answers are:
\[ x = 18, \quad (2x)° = 36°, \quad \text{and} \quad (3x)° = 54° \]