Number of rotations

Geometry Level 3

Let $$f (x)$$ be the relation from $$N->$${$$5,10$$} equal to $$10^{\circ}$$ when $$x$$ is odd and $$5^{\circ}$$ when $$x$$ is even. Here $$x$$ denotes $$x^\text{th}$$ rotation of point $$(2,5)$$ and $$f (x)$$ is angle rotated clockwise by this $$x^\text{th}$$ rotation when rotated about the point $$(8,15)$$. If after $$a$$ rotations, the final point is again $$(2,5)$$, find the minimum value of $$\frac {a}{2}$$.

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