This problem involves finding the value of $x$ where the angles are given as $2x$, $3x$, and $4x$. Since these are angles of a triangle, the sum of the angles must equal $180^\circ$.

Let's set up the equation:

$2x + 3x + 4x = 180^\circ$

Simplifying:

$9x = 180^\circ$

Now, solve for $x$:

$x = \frac{180^\circ}{9} = 20^\circ$

Thus, the value of $x$ is $20^\circ$, which corresponds to option C.

Do you want more details or have any questions?

Here are some related questions for practice:

1. If the angles were $2x$, $5x$, and $6x$, what would $x$ be?
2. What is the sum of the interior angles in a quadrilateral?
3. How do you find the value of angles in polygons?
4. Can a triangle have angles with a ratio of $1:2:3$? If so, what are the angles?
5. If the angles were listed as $x+10$, $2x$, and $3x$, how would you solve for $x$?

Tip: Always remember that the sum of the angles in any triangle is $180^\circ$. This can help you solve for unknown angles.