In a triangle, the sum of the angle measures is always 180 degrees. Given the angles \( 75^\circ \), \( 41^\circ \), and \( (3x + 19)^\circ \), we can set up the following equation:
\[ 75 + 41 + (3x + 19) = 180 \]
Now, let's simplify the left side of the equation:
\[ 75 + 41 = 116 \] \[ 116 + (3x + 19) = 180 \]
So we have:
\[ 116 + 3x + 19 = 180 \]
Now, combine the constants:
\[ 135 + 3x = 180 \]
Next, isolate \( 3x \) by subtracting 135 from both sides:
\[ 3x = 180 - 135 \] \[ 3x = 45 \]
Now, divide both sides by 3:
\[ x = \frac{45}{3} = 15 \]
So the solution for \( x \) is:
\[ \boxed{15} \]
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