I recently found this problem in my maths book, and I don't know how I should solve it:

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I looked in the answers section of the book, and there it said that I should begin by using the law of cosines on the triangles ABD and BDC, and then use the fact that , as degrees. Why is that? Have I forgotten about some basic geometric rule or something?

And still, even after using the fact above, I couldn't complete the task. So how do I complete this task?