https://file.aiquickdraw.com/mathbot/file/17268355982201y0n933l.jpg

To determine which angles are adjacent from the diagram and the given question, let's first clarify the concept of adjacent angles. Adjacent angles share a common side and a common vertex but do not overlap.

### Step-by-step analysis:

- In the diagram, \( L\overline{N} \) and \( O\overline{Q} \) are parallel lines, and \( P\overline{R} \) is a transversal line cutting through them.
- The question asks which angles are adjacent.

### Given options:
1. \( \angle OPR \) and \( \angle QPR \)
2. \( \angle OPR \) and \( \angle QPM \)
3. \( \angle OPR \) and \( \angle LMP \)
4. \( \angle OPR \) and \( \angle NMP \)

#### Key identification:
- \( \angle OPR \) is located at point \( P \), and involves the rays \( \overline{OP} \) and \( \overline{PR} \), with vertex \( P \).
  
#### Checking adjacent angle pairs:
1. **\( \angle OPR \) and \( \angle QPR \)**: These angles share the ray \( \overline{PR} \) and vertex \( P \). Thus, they are adjacent.
2. **\( \angle OPR \) and \( \angle QPM \)**: These angles do not share a common ray or form at the same vertex.
3. **\( \angle OPR \) and \( \angle LMP \)**: These angles are formed at different vertices and do not share a common ray.
4. **\( \angle OPR \) and \( \angle NMP \)**: These angles are located at different vertices and do not share a common ray.

### Conclusion:
The correct adjacent angles are **\( \angle OPR \) and \( \angle QPR \)**, which corresponds to the first option.

Would you like further explanation or more details about adjacent angles? Here are some related questions:

1. What are the properties of parallel lines and transversals?
2. Can adjacent angles be complementary or supplementary?
3. How do you identify corresponding angles in this diagram?
4. How does the concept of vertical angles apply here?
5. What are alternate interior angles, and where can they be found in this diagram?

**Tip:** Adjacent angles always share a common side and vertex without overlapping.

Which angles are adjacent angles in the diagram where lines LN and OQ are parallel and a transversal PR intersects them?

This problem demonstrates how to identify adjacent angles formed by a transversal cutting through two parallel lines. Learn how to recognize adjacent angles in a geometric figure, including a step-by-step analysis of the correct angle pairs.

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