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To solve this problem, let's break it down step by step.

### Given Information:
1. The lines \( \overline{AB} \), \( \overline{CD} \), and \( \overline{EF} \) are parallel.
2. \( \angle FEB = 65^\circ \).
3. \( \angle EBD = 15^\circ \).
4. We are asked to find \( \angle CDB \).

### Approach:
1. **Parallel Lines and Transversal Property**: Since \( \overline{AB} \), \( \overline{CD} \), and \( \overline{EF} \) are parallel, we can apply the properties of angles formed by parallel lines and a transversal.

2. **Angle Relationships**:
   - \( \angle FEB = 65^\circ \) is an exterior angle with respect to the transversal through points \( E \), \( B \), and \( D \). The interior corresponding angle to this is \( \angle BDC \).
   - \( \angle EBD = 15^\circ \).

3. **Sum of Angles in a Triangle**:
   Triangle \( \triangle CDB \) will have the sum of its internal angles equal to \( 180^\circ \).

Now, I'll proceed with the calculations.The measure of \( \angle CDB \) is \( 100^\circ \).

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:

1. What are the properties of corresponding angles when dealing with parallel lines and a transversal?
2. How would the problem change if one of the lines wasn't parallel?
3. What is the relationship between interior and exterior angles in a triangle?
4. Can we solve this problem using alternate interior angles instead of corresponding angles?
5. How can we use the concept of supplementary angles to verify the answer?

**Tip**: When working with parallel lines, always look for corresponding and alternate interior angles to simplify angle calculations.

En la figura adjunta, AB, CD y EF son paralelas, m∠FEB=65° y m∠EBD=15°, entonces la m∠CDB es:

This problem involves determining the measure of ∠CDB using the properties of parallel lines and angles, including the Corresponding Angles Postulate and the Exterior Angle Theorem. Suitable for students in Grades 8-10.

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