# Triangle espacate

Geometry Level 4

Look at the transformation the isosceles triangle $$ABC$$ undergoes above. $$A, B$$ and $$D$$ are collinear, and so are $$A, C$$ and $$E$$. $$M$$ is the midpoint of $$BC$$ and $$\angle BAC = 20º$$. Suppose we do the same thing with triangle $$DEM$$ and so on, repeating the process indefinitely. How many times do we need to do this - including the first transformation - for the greater angle of the resulting triangle to be $$175^\circ$$?

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