what is the measure of angle ECD from this following triangle problem?

Question

In triangle ABC, AB is larger than BC.

Then, we choose point E outside the triangle such that BE=BC.

We extend line AB to D, such that BD=BC.

BF is angle bisector of angle ABC.

If DC is parallel to BF, what is the measure of angle ECD?

Answer 1

According to your drawing, the angle ECD is equal to the angle CBF, and the latter is half of the angle ABC.

All in all :

$$\hat{ECD}=\hat{ABC}/2$$

If you don't have any information on the angle ABC, then you wont find the angle ECD