https://file.aiquickdraw.com/mathbot/file/1729101377690jbjojqbb.jpg

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### **Problem Description:**
The question asks for the value of \(\angle BCD\). It states that **BA is parallel to DE** and some key angles are shown:
- \(\angle D = 150^\circ\) 
- \(\angle ABC = 100^\circ\)

### **Solution:**
Given that **BA \parallel DE** and \(BC\) is a transversal line intersecting these two parallel lines at points \(B\) and \(C\), we can apply the following **parallel line angle properties**:

1. **Alternate interior angles:**
   - Since \(BA \parallel DE\) and \(BC\) is the transversal, the angle at \(C\) (which is part of \(\angle BCD\)) and the angle at \(B\) (\(\angle ABC\)) are alternate interior angles.
   - This means:  
     \(\angle ABC = \angle BCD\)

2. **Angle calculation:**
   - \(\angle ABC = 100^\circ\)
   - Therefore, \(\angle BCD = 100^\circ\).

### **Answer:**
The correct value of \(\angle BCD\) is **100°**, but this is **not listed among the options**. Hence, the correct answer from the given choices would be:
- **Option (v) None of these.**

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**Related Questions to Explore:**
1. What is the sum of interior angles of a polygon with \(n\) sides?
2. How are alternate interior angles formed between two parallel lines and a transversal?
3. What are corresponding angles, and when are they equal?
4. How do we solve for unknown angles in a triangle using properties of parallel lines?
5. What is the exterior angle theorem in geometry?

**Tip:**  
When two lines are parallel, alternate interior angles formed by a transversal are always equal. This property is useful for solving many angle-related problems.

In the given figure, BA is parallel to DE. What is the value of ∠BCD?

Learn how to determine the value of angle BCD using properties of parallel lines and alternate interior angles. This geometry problem involves angles formed by a transversal cutting through two parallel lines. Suitable for students in Grades 9-10.

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