https://r2.erweima.ai/mathbot/image/17245929498746orhwns4.jpg

圖中，AB//CD，若角ABE=110及角BED=90，求x

Let's analyze the geometry of the image provided to solve for angle \( x \).

### Given:
1. \( AB \parallel CD \)
2. \( \angle ABE = 110^\circ \)
3. \( \angle BED = 90^\circ \)

### To Find:
Angle \( x \) at point \( D \) (i.e., \( \angle CDE = x \)).

### Solution:

Since \( AB \parallel CD \) and \( BE \) acts as a transversal, the corresponding angles formed by the transversal are equal. This means:

- \( \angle ABE \) and \( \angle CDE \) (which we are denoting as \( x \)) are corresponding angles.

Given that \( \angle ABE = 110^\circ \), it follows that:

\[
x = \angle CDE = \angle ABE = 110^\circ
\]

So, the value of \( x \) is **110 degrees**.

Would you like more details on this solution, or do you have any other questions?

### Related Questions:

1. What are corresponding angles in parallel lines and a transversal?
2. How do alternate interior angles relate when two lines are parallel?
3. Can you explain the properties of angles formed by parallel lines?
4. What are supplementary angles, and how do they apply to this problem?
5. How can the concept of parallel lines help in solving real-world problems?

**Tip:** In geometry, always look for parallel lines and transversals. Identifying these can often simplify angle calculations due to the properties of corresponding, alternate interior, and exterior angles.

Learn how to solve for angle x in geometry with AB parallel to CD. Given angles ABE = 110° and BED = 90°, find the value of angle x (CDE). This problem explores properties of corresponding angles formed by parallel lines and a transversal. Suitable for students in Grades 7-9.

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