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To determine which side of triangle \( \triangle XYZ \) is the longest, we need to use the relationship between the angles and the sides of a triangle. In any triangle, the side opposite the largest angle will be the longest side.

From the given image:
- \( \angle X = 62^\circ \)
- \( \angle Y = 55^\circ \)
- \( \angle Z = 63^\circ \)

Since \( \angle Z = 63^\circ \) is the largest angle, the side opposite \( Z \), which is \( XY \), must be the longest side.

Therefore, the correct answer is **A. \( XY \)**.

Would you like further explanation or details on this?

Here are some related questions:
1. How can you use the Law of Sines to verify this?
2. What would happen if two angles were equal in a triangle?
3. How do the internal angles of a triangle always sum up?
4. What is the significance of an isosceles triangle in determining side lengths?
5. How does the Law of Cosines differ from using angle-side relationships?

**Tip**: Always remember, in any triangle, the side opposite the largest angle is the longest.

Learn how to determine the longest side of triangle XYZ using angle-side relationships. This problem explores key concepts in triangle geometry, including the Largest Angle Theorem, which states that the side opposite the largest angle in a triangle is the longest. Suitable for students in Grades 6-8.

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