Step 1: Instead of introducing a variable $x$ and solving $9x=180$, express the largest angle directly as a fraction of the total angle sum.
Step 2: The angles are in ratio $2:3:4$, so the total number of "parts" is $2+3+4=9$ parts, and these parts together make up the full angle sum of a triangle, $180^\circ$.
Step 3: The largest angle corresponds to the ratio term $4$, so it represents $\frac{4}{9}$ of the total $180^\circ$.
Step 4: Largest angle $=\frac{4}{9}\times180^\circ=80^\circ$.
Step 5: Check: the three angles would be $\frac{2}{9}\times180=40^\circ$, $\frac{3}{9}\times180=60^\circ$, $\frac{4}{9}\times180=80^\circ$, and indeed $40+60+80=180^\circ$, confirming consistency.
\[\boxed{80^\circ}\]