https://file.aiquickdraw.com/mathbot/file/17284881207997cowjmh0.jpg

From the image, the question asks which angles are supplementary. Here's how to determine this:

- **Supplementary angles** are two angles whose sum is 180°. 
- Since \( KM \parallel NP \) and \( QO \) is a transversal line, some of these angles are either **interior** or **exterior** angles on the same side of the transversal.

Looking at the choices, let's consider:
- \( \angle NOQ \) and \( \angle KLO \) - These two angles lie on opposite sides of the transversal and are not a pair of interior angles on the same side, so they are not supplementary.
- \( \angle NOQ \) and \( \angle MLJ \) - \( \angle NOQ \) is an interior angle on the upper left side of the transversal, and \( \angle MLJ \) is an interior angle on the lower right side, so they are not supplementary.
- \( \angle NOQ \) and \( \angle POQ \) - These two angles are adjacent angles along the transversal, which form a straight line. Therefore, they are **supplementary**.
- \( \angle NOQ \) and \( \angle POL \) - These are angles on the opposite side of the transversal and do not sum to 180°.

Thus, the correct answer is **\( \angle NOQ \) and \( \angle POQ \)**.

Would you like further clarification or more details on any steps?

Here are five related questions to explore further:
1. What are the properties of parallel lines and transversals?
2. How do alternate interior angles relate to parallel lines?
3. What is the difference between supplementary and complementary angles?
4. How do you identify corresponding angles in parallel line diagrams?
5. What are vertically opposite angles, and how do they relate to this diagram?

**Tip:** When working with parallel lines, remember that interior angles on the same side of the transversal are always supplementary.

Which angles are supplementary in the given diagram with parallel lines KM and NP, and transversal QO?

Learn how to identify supplementary angles in a diagram involving parallel lines (KM and NP) and a transversal (QO). Understand the properties of parallel lines, transversals, and how supplementary angles sum to 180°. Suitable for students in Grades 6-8.

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