To find the value of \( x \), we first use the fact that the sum of the angles in a triangle is \( 180^\circ \).
We are given the angles:
- \( 75^\circ \)
- \( 41^\circ \)
- \( (3x + 19)^\circ \)
We can set up the equation:
\[ 75 + 41 + (3x + 19) = 180 \]
Now, we first simplify the left side:
\[ 75 + 41 = 116 \]
So the equation becomes:
\[ 116 + (3x + 19) = 180 \]
Next, we simplify further by combining \( 116 \) and \( 19 \):
\[ 116 + 19 = 135 \]
Now, the equation is:
\[ 135 + 3x = 180 \]
To isolate \( 3x \), we subtract \( 135 \) from both sides:
\[ 3x = 180 - 135 \]
Calculating the subtraction:
\[ 3x = 45 \]
Now, we divide both sides by \( 3 \) to find \( x \):
\[ x = \frac{45}{3} = 15 \]
Thus, the solution is:
\[ \boxed{15} \]
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