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In this problem, we are given a triangle \( \triangle BDC \) with angles labeled, and lines \( AN \parallel ED \parallel FC \). We are asked to find the value of \( x \).

### Solution:

1. Since \( AN \parallel ED \parallel FC \), this setup suggests that we can use the concept of **transversals** and **corresponding angles** to find unknown angles in the triangle.

2. In \( \triangle BDC \):
   - The angle \( \angle DBC = x \).
   - We know \( \angle BCD = 50^\circ \).
   - The angle \( \angle BDC = 80^\circ \).

3. The sum of the angles in any triangle is always \( 180^\circ \), so we apply this to \( \triangle BDC \):
   \[
   x + 80^\circ + 50^\circ = 180^\circ
   \]

4. Simplifying the equation:
   \[
   x + 130^\circ = 180^\circ
   \]
   \[
   x = 180^\circ - 130^\circ
   \]
   \[
   x = 50^\circ
   \]

### Answer:
The value of \( x \) is \( 50^\circ \), so the correct answer is **A) 50°**.

Would you like further details on this problem, or do you have any questions?

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Here are 5 related questions to further explore similar concepts:

1. How can we identify corresponding angles in parallel lines cut by a transversal?
2. Why is the sum of angles in any triangle always \( 180^\circ \)?
3. How would the problem change if \( ED \) were not parallel to \( AN \) and \( FC \)?
4. What are alternate interior angles, and how are they used in geometry?
5. How can knowing parallel lines help in calculating unknown angles in polygons?

**Tip:** Remember, whenever parallel lines are involved, look for ways to apply corresponding or alternate interior angles to simplify angle calculations!

From the figure, what is the value of x if AN ∥ ED ∥ FC?

Learn how to determine the unknown angle x in a triangle with parallel lines using the Triangle Angle Sum Theorem and properties of parallel lines. This problem involves angles and geometry concepts suitable for Grades 8-10.

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