Triangle Puzzle


Here you see an isosceles triangle with a top-angle of 20 degrees. Both base angles are 80 degrees. Straight lines are drawn from the base corners, at angles of, respectively, 60 and 50 degrees to the baseline. Find the value of angle X.
The only thing you need to know is that the sum of the angles of a triangle is always 180 degrees. No sine or cosine, nor other complicated stuff. The solution can be found with the help of a few helper lines. I would like you to send me your solution and the method you used, to find out how many different ways there are to arrive at the solution.





Hint

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