The ratio of the angles of a triangle is given as $2:3:4$. Since the sum of all angles in a triangle is always $180^\circ$, we can calculate the actual angles as follows:

1. Let the angles be $2x$, $3x$, and $4x$, where $x$ is a common multiplier.

2. The sum of the angles is: $2x + 3x + 4x = 180$ Simplify: $9x = 180$ Solve for $x$: $x = 20$

3. The angles of the triangle are: $2x = 40^\circ, \quad 3x = 60^\circ, \quad 4x = 80^\circ$

4. The largest angle is $80^\circ$.

Final Answer:

The largest angle is $80^\circ$.

Would you like a detailed step-by-step breakdown or have further questions?

Related Questions:

1. How can you verify the angles form a valid triangle?
2. What happens if the ratio changes to $1:2:3$?
3. How do you find the area of a triangle with these angles and one side given?
4. Why must the sum of angles in a triangle always be $180^\circ$?
5. How do angle ratios affect the classification of triangles (e.g., acute, obtuse)?

Tip:

Always check that the sum of the angles in a triangle equals $180^\circ$ to ensure calculations are correct!