Complementary angles are two angles whose measures add up to \(90^\circ\). Given the two angles are \( (x+3)^\circ \) and \( (4x-2)^\circ \), you can set up the following equation:
\[ (x + 3) + (4x - 2) = 90 \]
Now, simplify and solve for \(x\):
\[ x + 3 + 4x - 2 = 90 \] \[ 5x + 1 = 90 \] \[ 5x = 90 - 1 \] \[ 5x = 89 \] \[ x = \frac{89}{5} \] \[ x = 17.8 \]
Now substitute \(x\) back into the expressions for the angles:
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For the first angle: \[ x + 3 = 17.8 + 3 = 20.8^\circ \]
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For the second angle: \[ 4x - 2 = 4(17.8) - 2 = 71.2 - 2 = 69.2^\circ \]
To summarize, the equation of the angles measures is: \[ (x + 3) + (4x - 2) = 90 \] with \( x = 17.8 \), resulting in angles of \( 20.8^\circ \) and \( 69.2^\circ \).