It was after I drew another triangle as a reflection of the first one, that I saw a solution. The lines in the triangle converged with some diagonals of the 18-gon and with the lines in the reflected triangle.
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How to deduce a solution; I found a solution after I received a hint from Erjen Lefeber a Dutch professor in Maths. He pointed out that the isosceles triangle was a segment of an 18-gon. And by drawing a few diagonals I should easily read the answer. So I did! |
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The hint helped a lot, but wasn't
really the solution which was asked for in the question.
Drawing an 18-gon along with all the diagonals
can't really be considered a few helper lines. It was after I drew another triangle as a reflection of the first one, that I saw a solution. The lines in the triangle converged with some diagonals of the 18-gon and with the lines in the reflected triangle. |
So now it's easy to deduce all the angles. To see the solution you only need the two (red) helper lines (see above picture). To prove this converging of the lines, I had to check it in the 18-gon, to see this was really so, and it was. I leave you to solve this puzzle with the help of these hints and come up with the exact value of angle X.
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