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.

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°.