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In this problem, we have two congruent triangles, \( \triangle ABC \) and \( \triangle FDE \). Since the triangles are congruent, their corresponding angles are equal. 

### Given Information:
1. In \( \triangle ABC \):
   - \( \angle ACB = 108^\circ \)
   - \( \angle ABC = 48^\circ \)

2. In \( \triangle FDE \):
   - \( \angle EDF = y^\circ \)
   - \( \angle DFE = (2x - y)^\circ \)

### Steps to Solve:

1. **Find the Measure of \( \angle CAB \):**
   Since the sum of angles in a triangle is \( 180^\circ \), we can find \( \angle CAB \) as follows:
   \[
   \angle CAB = 180^\circ - \angle ACB - \angle ABC = 180^\circ - 108^\circ - 48^\circ = 24^\circ
   \]

2. **Corresponding Angles:**
   Since \( \triangle ABC \cong \triangle FDE \), the angles in \( \triangle FDE \) are:
   - \( \angle FDE = \angle CAB = 24^\circ \)
   - \( \angle EDF = \angle ABC = 48^\circ \)
   - \( \angle DFE = \angle ACB = 108^\circ \)

3. **Set up an Equation for \( 2x - y \):**
   We know from the corresponding angles that \( \angle DFE = 108^\circ \). Since \( \angle DFE = 2x - y \):
   \[
   2x - y = 108
   \]

4. **Use \( y = 48 \):**
   From the congruence, \( y = 48^\circ \).

5. **Substitute and Solve for \( x \):**
   Substitute \( y = 48 \) into the equation \( 2x - y = 108 \):
   \[
   2x - 48 = 108
   \]
   \[
   2x = 156
   \]
   \[
   x = 78
   \]

### Solution:
The value of \( x \) is \( 78 \).

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

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### Related Questions:
1. How do congruent triangles help in solving for unknown angles?
2. What is the significance of corresponding angles in congruent triangles?
3. Can this problem be solved without using congruence properties?
4. How can you check if two triangles are congruent in general?
5. What other geometric properties apply when two triangles are congruent?

### Tip:
Always remember that the sum of angles in any triangle is \( 180^\circ \), which can help find missing angles.

In the diagram, ΔABC ≅ ΔFDE. Given angles in ΔABC are 108° and 48°, and angles in ΔFDE are labeled y° and (2x - y)°. Find the value of x.

Learn how to find the value of x in a pair of congruent triangles ΔABC ≅ ΔFDE, where given angles in ΔABC are 108° and 48°. This solution uses the triangle sum property and corresponding angles in congruent triangles, suitable for students in Grades 8-10.

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