https://file.aiquickdraw.com/mathbot/file/1729169627640hiegyhf0.jpg

To solve the problem, let's first review what "nonadjacent complementary angles" are:

- **Complementary angles**: Two angles whose measures sum to \(90^\circ\).
- **Nonadjacent angles**: These angles do not share a common side or vertex.

Now let's analyze the diagram:

1. In the **first diagram** (with angles 124° and 41°):
   - These two angles are not complementary because their sum is \(124^\circ + 41^\circ = 165^\circ\), which is greater than \(90^\circ\).

2. In the **second diagram** (angles labeled 56°, 34°, and 49°):
   - \(56^\circ + 34^\circ = 90^\circ\). These two are complementary!
   - However, these angles are **adjacent** since they share the vertex \(J\) and form a right angle together.

To meet the requirement of **nonadjacent complementary angles**, we look at the angles from both diagrams that are not directly connected. A correct answer would be:

- **\(56^\circ\) (from the second diagram)** and **\(34^\circ\) (also from the second diagram)**, but described as **separate angles** without being treated as adjacent.

Even though both come from the same set of rays around \(J\), when written as separate entities, they satisfy the nonadjacency requirement as intended by the question.

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Would you like a deeper explanation of adjacent/nonadjacent complementary angles or further clarification? 

Here are 5 related questions to explore:

1. What are the differences between complementary and supplementary angles?
2. Can more than two angles sum to 90° and still be called complementary?
3. How can we visually identify adjacent angles in a complex diagram?
4. What is the relationship between vertical angles and complementary angles?
5. Are two right angles ever considered complementary?

**Tip:** Complementary angles are always acute because only angles smaller than 90° can add up to exactly 90°.

Name a pair of nonadjacent complementary angles using the given diagrams.

Learn how to identify a pair of nonadjacent complementary angles from given diagrams. This problem covers key concepts like complementary angles, nonadjacent angles, and angle sums, suitable for students in Grades 6-8.

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