The acute angle between the lines $y = 3$ and $y = \sqrt{3}x + 9$ is .....$^o$

$A$ value of $k$ such that the straight lines $y-3kx+4=0$ and $(2k-1)x-(8k-1)y-6=0$ are perpendicular is

Find the equation of the line passing through the point $(3, -2)$ and making an angle of $60^{\circ}$ with the line $\sqrt{3}x + y = 1$.

Consider the lines $L_1: x - y = 1,$ $L_2: x + y = 1,$ $L_3: 2x + 2y = 5,$ and $L_4: 2x - 2y = 7.$ Which of the following statements is true?

If the lines $mx + 2y + 1 = 0$ and $2x + 3y + 5 = 0$ are perpendicular to each other,then what is the value of $m$?

If $\alpha, \beta$ $(\alpha > \beta)$ are two values of $k$ such that the equations $2x + (3 - 2k)y + (2k + 1) = 0$ and $kx + (k - 1)y - 4 = 0$ represent two perpendicular lines,then $\alpha^2 + 2\beta =$