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 \( \angle BAC = 20ยบ \). 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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