Thank you for pointing that out. Let's revisit the problem to ensure accuracy.

Given:

- \( \angle AOC = 160^\circ \) is a central angle.
- We need to find \( \angle ABC \), which is an inscribed angle subtending the same arc \( AC \).

### Correct Relationship:
- The inscribed angle \( \angle ABC \) is indeed supposed to be half of the central angle \( \angle AOC \), because they subtend the same arc \( AC \).

However, there's one possible mistake to consider. If the angle you are referring to as \( \angle ABC \) (the one marked in your solution) is incorrectly identified or there's an additional detail in the solution key, let's think about other potential details that might be affecting the interpretation. 

But normally, with the given information:
\[
\angle ABC = \frac{1}{2} \times \angle AOC = \frac{1}{2} \times 160^\circ = 80^\circ
\]

### If the solution key states \( \angle ABC = 100^\circ \):
- This might suggest that there is a misinterpretation of the angles or possibly a different segment or relationship being considered that we haven't accounted for with the current information.

Could you please clarify if there are any additional details in the solution or if any other angles were mentioned in the explanation? If not, the correct calculation should yield \( 80^\circ \), based on the given diagram.

Would you like to explore any other aspects or verify this with more information?

---

Here are 5 questions to consider:

1. Could the problem involve a different angle or triangle not clearly visible in the diagram?
2. Is there a specific context or theorem that could lead to the angle \( 100^\circ \)?
3. Could the solution have additional steps or a different interpretation of the diagram?
4. Are there other angles or circles in the problem that we might not be considering?
5. Could there be a mislabeling in the problem or solution key?

**Tip**: Always ensure that the angle being calculated is clearly identified, especially when dealing with inscribed and central angles, as misinterpretation can lead to confusion.

Explore the relationship between central and inscribed angles in geometry. Learn how to calculate inscribed angles like \( \angle ABC \) based on the given central angle \( \angle AOC \). Discover the inscribed angle theorem and its application in solving geometric problems. Suitable for high school students studying geometry.

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