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Let's analyze the problem step by step.

We are given a figure where \( q \) is a transversal of the parallel lines \( l \), \( m \), \( n \), and \( p \). The angles formed by the transversal with these lines are labeled as \( x^\circ \), \( 30^\circ \), and \( y^\circ \).

### Understanding the Relationships:
- **Alternate Interior Angles**: These angles are equal when a transversal crosses parallel lines.
- **Corresponding Angles**: These angles are also equal when a transversal crosses parallel lines.
- **Linear Pair**: The angles on a straight line sum up to 180°.

### Step 1: Use Alternate Interior Angles
Since \( l \parallel p \) and \( q \) is the transversal:
- The angle \( x^\circ \) is alternate to the angle \( y^\circ \).

So, \( x = y \).

### Step 2: Use Linear Pair
Given that the angle between lines \( m \) and \( n \) on the transversal is \( 30^\circ \), and the adjacent angle is \( y^\circ \), we can write:

\[
y + 30^\circ = 180^\circ
\]

\[
y = 150^\circ
\]

### Step 3: Conclude for \( x \)
Since \( x = y \), it follows that:

\[
x = 150^\circ
\]

### Final Answer:
The correct values of \( x \) and \( y \) are \( x = 150^\circ \) and \( y = 150^\circ \). Therefore, the correct answer is:

\[
\boxed{D} \quad x = 150^\circ, \ y = 150^\circ
\]

Would you like more details on any part of the solution?

### Relative Questions:
1. How do alternate interior angles relate to parallel lines?
2. What is the significance of corresponding angles in parallel lines?
3. Can you explain how the linear pair relationship works in this problem?
4. How would the solution change if \( y \) were given instead of \( 30^\circ \)?
5. What are some other properties of transversals with parallel lines?

### Tip:
When working with parallel lines and a transversal, always look for alternate interior angles and corresponding angles first, as these relationships can simplify the problem significantly.

In the figure shown, line q is a transversal of parallel lines l, m, n, and p. What are the values of x and y?

Learn how to determine the values of angles when a transversal intersects parallel lines. This problem covers key geometric concepts, including alternate interior angles and the linear pair relationship. Suitable for students in Grades 7-9.

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