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To find the value of \( x \) in the given diagram, we need to carefully analyze the angles provided and apply geometric angle relationships. 

### Key observations:
1. The angle at \( D \) is given as \( 115^\circ \).
2. The angle at \( C \) is \( 80^\circ \).
3. The angle at \( B \) is \( 65^\circ \), and since \( AB \) is perpendicular to the horizontal line at \( A \), the angle \( \angle ABC = 90^\circ \).
4. Angle \( E \) appears to be adjacent to \( x \), forming a linear pair on the straight line passing through \( A \) and \( E \).

### Step-by-step solution:

1. **Angle \( D \):** 
   The sum of angles on a straight line is \( 180^\circ \). So, at point \( D \), the angle adjacent to \( 115^\circ \) is:
   \[
   \angle DCE = 180^\circ - 115^\circ = 65^\circ.
   \]

2. **Angle \( C \):**
   Now, the sum of angles at point \( C \) in triangle \( ABC \):
   \[
   \text{Sum of angles in } \triangle ABC = 180^\circ.
   \]
   Therefore, the third angle at \( C \) in triangle \( ABC \) is:
   \[
   \angle ACB = 180^\circ - 90^\circ - 65^\circ = 25^\circ.
   \]

3. **Linear Pair at \( E \):**
   Since angles \( \angle EAC \) and \( x \) form a linear pair, their sum must be \( 180^\circ \). The angle \( EAC \) is equal to \( \angle CED \), which is given as \( 80^\circ \). Therefore, \( x \) can be calculated as:
   \[
   x = 180^\circ - 80^\circ = 100^\circ.
   \]

Thus, the value of \( x \) is \( \boxed{100^\circ} \).

Would you like further clarification on any part of the solution? Here are 5 related questions to explore:

1. What are the properties of linear pairs in geometry?
2. How can you find missing angles in a triangle using the sum of angles?
3. What is the significance of supplementary angles in this diagram?
4. How do perpendicular lines affect the angle measures in geometric shapes?
5. Can you apply the concept of exterior angles to any part of this figure?

**Tip:** Always check if the angles in a geometric figure form a straight line or a triangle, as these give helpful clues for solving problems.

Find the value of x in the provided geometry diagram.

In this geometry problem, you will learn how to find the value of x using the triangle angle sum theorem and the properties of supplementary angles. The given angles are 80°, 65°, and 115°, and we walk through the solution step-by-step to arrive at x = 100°.

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