ANSWER
[tex]80\degree[/tex]EXPLANATION
We want to find the measure of the largest angle of the triangle.
The sum of angles in a triangle is 180 degrees. This means that:
[tex]2x+3x+4x=180[/tex]Simplify the equation and solve for x:
[tex]\begin{gathered} 2x+3x+4x=180 \\ 9x=180 \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]The largest angle is 4x. Therefore, the measure of the largest angle is:
[tex]\begin{gathered} 4\cdot20 \\ 80\degree \end{gathered}[/tex]