If \(2x = 120^\circ\) is a corresponding angle, let's reconsider the scenario with this new information. This implies that we have to solve for the values of \(x\), \(y\), and the angles \(A\), \(B\), and \(C\) in the isosceles triangle \(ABC\).

### Step-by-Step Solution

Given:

- \(2x = 120^\circ\) (since it’s a corresponding angle).
- The triangle \(ABC\) is isosceles, so \( \angle A = \angle B \).
- Let's assume \( \angle A = y \) and \( \angle B = y \), then \( \angle C = 180^\circ - 2y \).

### Finding \(x\):

Since \(2x = 120^\circ\):

\[
x = \frac{120^\circ}{2} = 60^\circ
\]

### Finding \(y\):

Since the triangle is isosceles, \( \angle A = \angle B = y \), and using the triangle sum property:

\[
y + y + (180^\circ - 2y) = 180^\circ
\]

\[
2y + 180^\circ - 2y = 180^\circ
\]

This equation confirms that \( \angle C = 180^\circ - 2y \). 

However, since \( \angle B \) corresponds to \( 120^\circ \), let's analyze:

Given that \(2x = 120^\circ\), then \(x = 60^\circ\). So, \( y = 60^\circ \).

Finally, let's determine the angles:

- \( \angle A = y = 60^\circ \)
- \( \angle B = y = 60^\circ \)
- \( \angle C = 180^\circ - 2y = 180^\circ - 120^\circ = 60^\circ \)

### Conclusion:

All angles \( \angle A \), \( \angle B \), and \( \angle C \) are \( 60^\circ \), making \( \triangle ABC \) an **equilateral triangle**.

### Final Values:
- \( \angle A = 60^\circ \)
- \( \angle B = 60^\circ \)
- \( \angle C = 60^\circ \)

Would you like further details or have any questions?

### Relative Questions:
1. What are the properties of an equilateral triangle?
2. How do corresponding angles influence the solution of a triangle?
3. What is the relationship between angles in an equilateral triangle?
4. How does the triangle sum property apply in different types of triangles?
5. How do different angle properties (e.g., corresponding, alternate) affect triangle problems?

**Tip:** In an equilateral triangle, all three angles are equal to \( 60^\circ \) and all sides are of equal length.

Explore how corresponding angles influence triangle properties. Solve the problem 2x = 120° to determine angles in an isosceles triangle. Discover key concepts including the triangle sum property and implications of corresponding angles.

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