The inclination of the straight line passing through the point $A(-3, 6)$ and the mid-point of the line joining the $B(4,-5)$ and $C(-2,9)$, with $x-$axis is

The coordinates of the mid-point $D$ of line segment $BC$ are $(1, 2).$

$\therefore$ Slope of $AD=\frac{6-2}{-3-1}=-1$

$\Rightarrow \tan \theta =-1$, where $\theta$ is the angle made by $AD$ with $x-$axis

$\Rightarrow \theta =\frac{3\pi }{4}$

So, $AD$ makes angle $\frac{3\pi }{4}$ with $x-$axis.