Find the value of $\angle x$

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Question:

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There are no data other than the data in the image

My Approach:

After a lot of time, I was only able to find two isosceles triangles as in the picture.

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Thank you for attending to my question!

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Only one hint, rest is straight-forward.

image

Apply Menelaus's theorem in triangles $ACB,$ $ADB,$ $ACD$ with respect to the traversal $FEH$. This leads you to the fact that $\triangle GDE$ is isosceles.