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I tried a lot. Currently, I know the answer but I want to know how to solve it.

I need a mathematical or geometrical solution, not by measuring by any instrument.

DG_
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    Since you say you tried a lot, please include one or two tries you've made directly in your post. – amWhy Sep 29 '17 at 15:01
  • See also https://math.stackexchange.com/questions/799790/simplest-known-solution-to-worlds-hardest-easy-geometry-problem and references therein. This version is the "second hardest elementary geometry problem" so not quite a duplicate but close. – NickD Sep 29 '17 at 21:13

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I have three different solutions and one general solution to your problem: enter image description here

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amWhy
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Seyed
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  • What software did you use to write this answer? –  Oct 03 '17 at 21:00
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    @Jack, I used the $Free$ C.a.r software to draw and typed in paint. You can download the software from here: http://car.rene-grothmann.de/doc_en/download.html – Seyed Oct 03 '17 at 23:26
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Hint: Start with the triangle with $50$ and $60$ degrees to obtain $70$. Then use the straight line angle $180=z+70$ to obtain the adjacent angles. Then use $360=70+110+110+w$ to find the last angle of the crossing.

MrYouMath
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