In the given triangle, we have the following angles:

• One angle is $60^\circ$,
• Another angle is $3x$,
• The third angle is $x$.

To find the value of $x$, we can use the fact that the sum of the angles in any triangle is $180^\circ$. Therefore, the equation for the sum of the angles is:

$60^\circ + 3x + x = 180^\circ$

Simplifying this equation:

$60^\circ + 4x = 180^\circ$

Now, subtract 60 from both sides:

$4x = 120^\circ$

Finally, divide by 4:

$x = 30^\circ$

Thus, the value of $x$ is $30^\circ$.

Would you like further details or have any questions?

Here are five related questions to expand on this:

1. What would the equation be if the known angle was $70^\circ$ instead of $60^\circ$?
2. How can you check if your solution is correct by substituting $x = 30^\circ$ into the angles of the triangle?
3. What would the angles of the triangle be if $x = 25^\circ$?
4. How do we know the sum of angles in any triangle is always $180^\circ$?
5. How would you solve a similar problem with an isosceles triangle?

Tip: Always verify your answers by checking that the angles sum to $180^\circ$ after solving for unknowns in triangles.