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We are given a diagram where \( AB \parallel CD \), and we need to find the value of angle \( x \). Let's break this down:

### Step 1: Parallel Lines and Corresponding Angles
Since \( AB \parallel CD \) and the transversal is \( AE \), the angle \( \angle AEB = 20^\circ \) and \( \angle CDE = 130^\circ \) are related to the angles at \( A \) and \( C \).

- The angle \( \angle BAE \) is formed between the transversal \( AE \) and the line \( AB \). Therefore, by the corresponding angles theorem (because \( AB \parallel CD \)), the angle at \( A \) corresponding to \( \angle CDE \) will be \( 130^\circ \) as well.

### Step 2: Angles in a Triangle
Now, looking at triangle \( AEC \), we know that the sum of the internal angles of any triangle is \( 180^\circ \). In this triangle, we have:
- \( \angle AEB = 20^\circ \) (given),
- \( \angle CED = 130^\circ \),
- And the angle \( x \) at \( A \) is what we need to find.

The sum of these angles should equal \( 180^\circ \):
\[
x + 130^\circ + 20^\circ = 180^\circ
\]

### Step 3: Solving for \( x \)
\[
x + 150^\circ = 180^\circ
\]
\[
x = 180^\circ - 150^\circ
\]
\[
x = 30^\circ
\]

Thus, the value of \( x \) is \( 30^\circ \).

Would you like any further clarifications or additional details? 

Here are some related questions to expand your understanding:
1. How do corresponding angles help in parallel line problems?
2. Can you apply the concept of alternate interior angles to this problem?
3. How would the calculation change if angle \( \angle CED \) was different?
4. What are other ways to find angles in geometrical shapes involving parallel lines?
5. Can you explore how to solve such problems in 3D geometry?

**Tip:** Always remember that the sum of the angles in a triangle is \( 180^\circ \), which is fundamental in solving many geometrical problems!

In the given figure, AB || CD. Find the value of x.

Learn how to find the value of angle x in a geometric problem involving parallel lines AB || CD, and a transversal. This problem uses the corresponding angles theorem and the triangle angle sum theorem. Suitable for students in Grades 7-9.

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