Explanation

(b)
The slopes of the lines of regression of $y$ on $x$ and $x$ on $y$ are $m_{1} = b_{yx}\ and\ m_{2} = \frac{1}{b_{xy}}$respectively. Therefore, the angle between them is given by
$tan\theta = \frac{m_{1} - m_{2}}{1 + m_{1}m_{2}} = \frac{b_{yx} - \frac{1}{b_{xy}}}{1 + \frac{b_{yx}}{b_{xy}}}$
$\Rightarrow \theta = \tan^{- 1}\left( \frac{b_{yx} \times b_{xy} - 1}{b_{yx} + b_{xy}} \right)$