Problem: 100 degree Isosceles Triangle

Given an isoscles triangle ABC with AB = AC and the measure of angle BAC = 100 degrees. Extend AB to point D such that AD = BC. Now draw segment CD. What is the size of angle BCD?

Note: There can be several different approaches to this problem.

Ususally, a solution to a problem such as this requires some auxilliary constructions.
Do you want a Hint for one auxillary construction?