Solution:

We are tasked with finding $\angle EFD$ using the given information:

1. $AB \parallel CD$
2. $AF \parallel ED$
3. $\angle AFC = 68^\circ$
4. $\angle FED = 42^\circ$

Step-by-step explanation:

1. Identify the relationships using parallel lines:

   • Since $AB \parallel CD$, the transversal $AC$ implies that: $\angle AFC + \angle EFD = 180^\circ \quad \text{(linear pair or co-interior angles)}.$

2. Calculate $\angle EFD$: $\angle EFD = 180^\circ - \angle AFC = 180^\circ - 68^\circ = 112^\circ.$

3. Verify the consistency with other information:

   • The parallelism of $AF \parallel ED$ ensures that the angles are consistent as alternate or corresponding angles, validating that the calculated $\angle EFD$ is correct.

Final Answer:

$\boxed{\angle EFD = 112^\circ}$

Would you like more details on the derivation or further help with related concepts?

Related Questions:

1. What is the definition of co-interior angles and how do they relate to parallel lines?
2. How would the problem change if $AF$ and $ED$ were not parallel?
3. Can you explain alternate interior angles in this setup?
4. What are the properties of a transversal line cutting parallel lines?
5. How would the geometry change if the angles were given differently?

Tip:

When dealing with parallel lines and angles, always look for linear pairs, corresponding angles, and alternate interior angles to simplify the problem.