Complementary angles are two angles whose measures add up to 90 degrees. Given that the measures of the two angles are \(3x\) and \(4x + 1\), we can set up the equation as follows:
\[ 3x + (4x + 1) = 90 \]
Now, let's simplify the equation:
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Combine like terms: \[ 3x + 4x + 1 = 90 \]
This simplifies to: \[ 7x + 1 = 90 \]
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Next, we subtract 1 from both sides: \[ 7x = 89 \]
So, the simplified equation corresponding to the measures of the angles is: \[ 7x + 1 = 90 \]