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We are given that \( \overleftrightarrow{CE} \) and \( \overleftrightarrow{FH} \) are parallel lines, and \( m\angle FGD = 56^\circ \). We need to determine \( m\angle CDB \).

### Step-by-step solution:

1. **Identify corresponding angles:**
   Since \( \overleftrightarrow{CE} \parallel \overleftrightarrow{FH} \), and \( \overleftrightarrow{BD} \) is a transversal, the angles \( \angle FGD \) and \( \angle CDB \) are **corresponding angles**.

2. **Corresponding angles theorem:**
   According to the corresponding angles theorem, corresponding angles formed by a transversal cutting through two parallel lines are congruent. Therefore:
   \[
   m\angle CDB = m\angle FGD
   \]
   
3. **Substitute the given value:**
   We are given that \( m\angle FGD = 56^\circ \), so:
   \[
   m\angle CDB = 56^\circ
   \]

Thus, the measure of \( \angle CDB \) is \( 56^\circ \).

Would you like further details, or have any questions about this explanation?

Here are 5 related questions you might consider:
1. What are alternate interior angles and how do they apply in similar problems?
2. How can we prove that two lines are parallel using angles formed by a transversal?
3. If \( m\angle FGD \) had been \( 40^\circ \), what would \( m\angle CDB \) be?
4. How do supplementary angles factor into problems involving parallel lines and transversals?
5. How could you identify whether two angles are vertically opposite in a diagram like this?

**Tip:** When working with parallel lines and a transversal, remember that both alternate interior angles and corresponding angles are congruent.

If CE and FH are parallel lines and m∠FGD = 56°, what is m∠CDB?

Explore how to find the measure of angle CDB when given that lines CE and FH are parallel, and m∠FGD = 56°. This problem applies the corresponding angles theorem and is suitable for students in grades 8-10.

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