From where do I start the chase?

Geometry Level 5

Consider an isosceles \( \Delta ABC \) with points \( E_{1}, E_{3}, E_{5}, \cdots E_{99} \) on side \( AC \) and points \( E_{2}, E_{4}, E_{8}, \cdots E_{100} \) on side \( AB \) such that \( AE_{1} = E_{1}E_{2} = E_{2}E_{3} = \cdots = E_{99}E_{100} = E_{100}C = BC \). Now, \( \angle BAC \) , in degrees, is of the form \( \dfrac{x}{y} \) where \( x \) and \( y \) are coprime natural numbers. Find \( x+y-72 \).

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