100 degree isosceles triangle

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 measure of angle BCD? Prove your results by geometric reasoning, rather than measuring.

Note: There can be several different approaches to this problem. Geometric arguments are preferred to using trigonometry.

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