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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.

Write an equation for the sum of the angles in this triangle. Use your equation to find the value of x.

Learn how to find the value of x in a triangle where the angles are given as 60°, 3x, and x. This solution uses the sum of angles in a triangle theorem and basic algebra to solve for x. Suitable for students in Grades 6-8.

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