Complementary angles are two angles that sum up to 90 degrees. Given the angles \( (x+3)^\circ \) and \( (4x-2)^\circ \), you can set up the equation as follows:
\[ (x + 3) + (4x - 2) = 90 \]
Now, let's simplify the equation:
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Combine like terms: \[ x + 3 + 4x - 2 = 90 \]
This simplifies to: \[ 5x + 1 = 90 \]
So, the finalized equation of the angle measures is:
\[ (x + 3) + (4x - 2) = 90 \]