The acute angle between the lines given by $y - \sqrt{3}x + 1 = 0$ and $\sqrt{3}y - x + 7 = 0$ is (in $^{\circ}$)

If $A(-3,3), B(1,1), C(1,-1)$ and $D(-2,-2)$ are the vertices of a quadrilateral,the angle between the diagonals $AC$ and $BD$ 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 slope of a line $L$ is $2$. If $m_1$ and $m_2$ are the slopes of two lines which are inclined at an angle of $\frac{\pi}{6}$ with $L$,then $m_1 + m_2 =$

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

Let the angle between the lines $x-2y+3=0$ and $kx-y+2=0$ be $45^{\circ}$. If $k_1, k_2$ $(k_1 > k_2)$ are two distinct real values of $k$,then $k_1-2=$