The angle between the straight lines $x - y\sqrt{3} = 5$ and $\sqrt{3}x + y = 7$ is ............. $^\circ$.

$A$ line $L$ passing through the point $(2,0)$ makes an angle $60^{\circ}$ with the line $2x-y+3=0$. If $L$ makes an acute angle with the positive $X$-axis in the anticlockwise direction,then the $Y$-intercept of the line $L$ is:

The acute angle between two straight lines passing through the point $M(-6, -8)$ and the points in which the line segment $2x + y + 10 = 0$ enclosed between the coordinate axes is divided in the ratio $1 : 2 : 2$ in the direction from the point of its intersection with the $x$-axis to the point of intersection with the $y$-axis is:

The slopes of the lines,making an angle of $45^{\circ}$ with the line $2x - 3y = 5$,are

The angle between the line $x+y=3$ and the line joining the points $(1,1)$ and $(-3,4)$ is

If the lines $y = 3x + 1$ and $2y = x + 3$ make equal angles with the line $y = mx + 4$,then $m = $ . . .