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We are given that \( AB \parallel DE \), \(\angle ABC = 120^\circ\), and \(\angle CDE = 135^\circ\). We are asked to find \(\angle BCD\).

Let's break it down step by step:

1. Since \( AB \parallel DE \) and \( BC \) is a transversal, the corresponding angles theorem tells us that:
   \[
   \angle ABC + \angle BCD = 180^\circ
   \]
   because they form a linear pair.

2. Given \(\angle ABC = 120^\circ\), we can substitute this into the equation to find \(\angle BCD\):
   \[
   \angle BCD = 180^\circ - 120^\circ = 60^\circ
   \]

Thus, \(\angle BCD = 60^\circ\).

Would you like further details or clarification on this solution?

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### Related Questions:
1. What is the corresponding angles theorem, and why does it apply here?
2. How do parallel lines affect the angles formed by a transversal?
3. What is the sum of the interior angles of a triangle, and how can it be applied to find unknown angles?
4. If \(\angle CDE = 135^\circ\), what can you infer about \(\angle CEB\) if \( BC \) is extended further?
5. What other properties of parallel lines are useful for solving geometry problems like this?

### Tip:
In problems with parallel lines, always look for pairs of corresponding, alternate interior, or co-interior angles—they can help simplify complex figures.

In the given figure, if AB is parallel to DE, angle ABC = 120° and angle CDE = 135°, then find angle BCD.

Learn how to find angle BCD given parallel lines AB and DE, with angles ABC = 120° and CDE = 135°. The solution involves the Corresponding Angles Theorem and the Linear Pair Theorem. Suitable for Grades 8-10.

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