Number of rotations

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 $\frac {a}{2}$ .