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In the provided image, the problem shows two parallel lines, with transversals intersecting at angles. The goal is to find the values of \( y \) and \( x \).

### Step-by-Step Solution:

1. **Identify Corresponding and Alternate Angles:**
   - Since \( h \parallel j \parallel k \), the given angles are either corresponding or alternate interior angles.

2. **Relation Between Angles:**
   - The angle labeled \( (4x - 33)^\circ \) and the angle labeled \( 83^\circ \) are corresponding angles. Thus, we can set up an equation:
   \[
   4x - 33 = 83
   \]
   Solving for \( x \):
   \[
   4x = 83 + 33
   \]
   \[
   4x = 116
   \]
   \[
   x = \frac{116}{4} = 29
   \]

3. **Find the Value of \( y \):**
   - The angle labeled \( y^\circ \) is vertically opposite to the angle \( 83^\circ \), so they are equal:
   \[
   y = 83
   \]

### Final Answers:
- \( x = 29 \)
- \( y = 83 \)

Would you like further details or have any additional questions?

### 5 Related Questions:
1. What are corresponding angles, and how are they used in parallel line problems?
2. How can alternate interior angles help in solving transversal problems?
3. Can you provide another example where the sum of angles on a straight line is used?
4. What are vertically opposite angles, and why are they always equal?
5. How do parallel lines affect the angles formed by a transversal?

### Tip:
Always look for relationships like corresponding, alternate interior, and vertically opposite angles when dealing with parallel lines and transversals.

En la figura, h || j || k. Hallar los valores de y y x.

Learn how to find the values of y and x in a problem involving parallel lines and transversals. Understand key concepts such as corresponding and vertical angles with a step-by-step solution. Suitable for students in Grades 7-9.

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