Question

The angle made by the straight line xcos (alpha) + ysin (alpha) = p with the negative direction of x axis

Answer 1

Given,
$x \cos( \alpha ) + y \sin( \alpha ) = p \\ > y \sin( \alpha ) = p - x \cos( \alpha ) \\ y = - \frac{ \cos( \alpha ) }{ \sin( \alpha ) } x + \frac{p}{ \sin( \alpha ) } \\ y = - \cot( \alpha ) x + \frac{p}{ \sin( \alpha ) } \\ y = \tan( \frac{\pi}{2} + \alpha )x + \frac{p}{ \sin( \alpha ) }$
According to slope intercept form of straight lines, angle between +ve x-axis and the given line is
$\frac{\pi}{2} + \alpha$
Therefore the same between -ve x-axis and given line is
$\pi - ( \frac{\pi}{2} + \alpha ) \\ = \frac{\pi}{2} - \alpha$
Hope this helps