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To solve for \( y \) and \( x \) in the given problem, we need to use the properties of parallel lines and the angles formed by a transversal.

### Analyzing the Figure

1. **Angle Relationships**:
   - Since \(\ell \parallel m\), the corresponding angles formed by the transversal are equal.
   - The given angles are:
     - \(80^\circ\)
     - \( (4x - 60)^\circ\)

### Step-by-Step Solution:

1. **Identify Corresponding Angles**:
   - The angle \(80^\circ\) and the angle \((4x - 60)^\circ\) are corresponding angles.
   - Therefore, we can set them equal to each other:
     \[
     80 = 4x - 60
     \]

2. **Solve for \( x \)**:
   - Start by isolating \( x \):
     \[
     80 + 60 = 4x
     \]
     \[
     140 = 4x
     \]
     \[
     x = \frac{140}{4}
     \]
     \[
     x = 35
     \]

3. **Determine the Value of \( y \)**:
   - The problem statement asks for \( y \) and \( x \).
   - \( y \) is not directly mentioned in the equation, but in many such problems, \( y \) could be another angle related to \( x \). Given no other direct relationship, if \( y \) is the angle corresponding to another transversal with the same lines, then it might also be \(80^\circ\).
   
### Final Answers:
\[
x = 35
\]
\[
y = 80^\circ \text{ (if the angle corresponding to the transversal)}
\]

Would you like further details or have any other questions?

Here are 5 related questions:
1. What are corresponding angles and how are they identified?
2. How can we use the properties of parallel lines to solve for unknown angles?
3. Can you explain how to solve linear equations?
4. What other angle relationships can be used when dealing with parallel lines and transversals?
5. How do you identify and solve for vertical angles?

**Tip**: Always remember that corresponding angles formed by a transversal cutting through two parallel lines are equal.

En la figura a continuación, si l || m, hallar los valores de y y x.

Learn how to find the values of x and y when two parallel lines are cut by a transversal. This problem involves the Corresponding Angles Postulate and solving linear equations. Suitable for students in Grades 8-10.

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