From where do I start the chase?

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 $x+y-72$ .