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This problem provides the measures of the angles of a triangle \( \triangle XYZ \) (\( m\angle X = 49^\circ \), \( m\angle Z = 81^\circ \), \( m\angle Y = 50^\circ \)) and asks for the length of a side \( x \). However, no sides of the triangle are given. Since all angles of the triangle are provided, the problem assumes the use of the Law of Sines to solve for \( x \).

### Law of Sines Formula:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}.
\]

Here, \( A \), \( B \), and \( C \) are the angles, and \( a \), \( b \), and \( c \) are the opposite sides. To determine the length of side \( x \), **at least one side length must be known**.

Since **no side length is provided**, the correct answer is:

**"There is not enough information to use the Law of Sines."**

### Let me know if you'd like a further explanation of this approach! 

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#### Related Questions:
1. What is the Law of Sines and when is it applicable?
2. How can the Law of Sines be used when at least one side length is given?
3. What is the relationship between the sum of the angles in a triangle and their sides?
4. How can you solve a triangle when all angles and one side are provided?
5. Can the Law of Sines help in solving right triangles?

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#### Tip:
Always check if you have at least one side length before applying the Law of Sines. This ensures the problem is solvable!

Triangle XYZ has the following measures: m∠X = 49°, m∠Z = 81°, and m∠Y = 50°. What is the length of side x?

Explore how to solve for the length of a side in triangle XYZ using the Law of Sines. Given the angles m∠X = 49°, m∠Z = 81°, and m∠Y = 50°, find out why it's necessary to have at least one side length to apply this method. Ideal for students in Grades 10-12.

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