Determinating the angle in a triangle

Question

Determine the value of the angle $\alpha$ of the figure below.

enter image description here

What are your thoughts on the problem so far? Which angles have you been able to determine? — Cameron Buie, Nov 01 '13 at 19:51
Hello Cameron I have determinated the angles $\angle DFC$, $\angle DFE$, $\angle DEF$, $\angle FBC$, $\angle DAC$ — Roiner Segura Cubero, Nov 01 '13 at 19:58

score 1 · Answer 1 · answered Nov 01 '13 at 19:57

This is a problem that is notoriously difficult to solve using elementary techniques. You might want to look at this solution.

For more information (and there is a lot) look under adventitious angles. The problem seems have been first published by Langley, so that could be another useful search term.

score 1 · Answer 2 · answered Nov 01 '13 at 20:01

1

This is a problem that I have solved before on my blog. I just post the solution and you will find the paths.

Hint: see $BFD$ equilateral triangle.

enter image description here

answered Nov 01 '13 at 20:01

newzad

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Determinating the angle in a triangle

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