To solve for \( x \) in the triangle with angle measures of \( 75^\circ \), \( 41^\circ \), and \( (3x + 19)^\circ \), we can use the fact that the sum of the angles in a triangle is always \( 180^\circ \).
We set up the equation:
\[ 75 + 41 + (3x + 19) = 180 \]
Now, combine the constant terms:
\[ 75 + 41 + 19 = 135 \]
So we have:
\[ 135 + 3x = 180 \]
Next, isolate \( 3x \) by subtracting \( 135 \) from both sides:
\[ 3x = 180 - 135 \]
\[ 3x = 45 \]
Now, divide both sides by \( 3 \):
\[ x = \frac{45}{3} = 15 \]
Thus, the solution for \( x \) is:
\[ \boxed{15} \]
11 answers