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Triangle Image enter image description here

How do I find $\angle\,\text{BCD}$? We know that $\text{AD} =\text{BC}$.

I just don't know how to find $\angle\,\text{BCD}$. I tried using parallel line but I just can't.

Andreas
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Jimmy
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  • You have seen that AB and AC is of equal length? – Andreas Mar 05 '17 at 12:13
  • sorry I don't what to call it when 2 side of a triangle is the same length. My English is not good – Jimmy Mar 05 '17 at 12:15
  • Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post. – Andreas Mar 05 '17 at 12:16
  • That is given by the context, at least in this case as the triangle is a isosceles triangle. You marked it right with your - in the sides of your triangle. I just wanted to check that you saw that fact. – Andreas Mar 05 '17 at 12:21
  • It's not a homework, though. I found this in some kind of Engineering test today. None of my friend can give answer to this. :( – Jimmy Mar 05 '17 at 12:22
  • It's okay to ask homework questions, just add what you have tried with and it will be okay. Sorry if I expressed myself a bit clumsy. – Andreas Mar 05 '17 at 12:34
  • Would you like to include a picture or link to this test? I'm interested. – Andreas Mar 05 '17 at 13:04
  • There's no link. It's a part of a Chulalongkorn University in Thailand Engineering event. They let us take the test home but it's all written in Thai. I'm afraid that I can't translate it well into English. – Jimmy Mar 06 '17 at 01:38

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let $$AD=x$$ and the angle $$BCD=y$$ then we get after the Theorem of sines $$\frac{\sin(100^{\circ}-y)}{\sin(80^{\circ})}=\frac{\sin(80^{\circ}-y)}{\sin(20^{\circ})}$$ can you solve this?

Dr. Sonnhard Graubner
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