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In the figure below, how can we find $x$ by geometrical arguments and without using sine-cosine formulae or co-ordinate geometry. And if it is not possible solely by geometrical arguments, then why is it not possible?

Figure

Note: Image not subject to scale. Numbers are for example purpose only, one can have any other numbers as well.

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I think the correct answer is $80^\circ$

I did it by geometrical construction.

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  • $\begingroup$ Can you add more details? $\endgroup$
    – Aditya Dev
    Apr 12, 2016 at 7:30
  • $\begingroup$ Can I add pictures as solution? $\endgroup$
    – ashi
    Apr 12, 2016 at 8:00

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