To solve this problem, we first recall the triangle angle sum theorem: the sum of the angles in a triangle is always 180°. The given angles are $60^\circ$, $3x$, and $x$.

Step 1: Write an equation for the sum of the angles

$60 + 3x + x = 180$

Step 2: Simplify the equation

Combine like terms: $60 + 4x = 180$

Step 3: Solve for $x$

Subtract $60$ from both sides: $4x = 120$

Divide by $4$: $x = 30$

Final Answer:

The value of $x$ is 30°.

Would you like further clarification or more examples? Here are some follow-up questions to enhance your understanding:

1. What happens if the given triangle is not specified to be a simple triangle (e.g., obtuse or right)?
2. Can the value of $x$ change if the given triangle is scaled differently in size?
3. How would the calculation change if one of the angle expressions included a subtraction?
4. Can a triangle exist if any angle exceeds 180°? Why or why not?
5. How can you verify your solution geometrically using these angle values?

Tip: Always check the angle sum to ensure the total is 180° to avoid errors in calculations.