The equation of one of the straight lines which passes through the point $(1, 3)$ and makes an angle of $\tan^{-1}(\sqrt{2})$ with the straight line $y + 1 = 3\sqrt{2}x$ is:

The angle between the lines $x - \sqrt{3}y + 5 = 0$ and the $y$-axis is ....$^o$

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

The angle between the lines $y = (2 - \sqrt{3})x + 5$ and $y = (2 + \sqrt{3})x - 7$ 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

Let $\theta_1$ be the angle between two lines $2x + 3y + c_1 = 0$ and $-x + 5y + c_2 = 0$,and $\theta_2$ be the angle between two lines $2x + 3y + c_1 = 0$ and $-x + 5y + c_3 = 0$,where $c_1, c_2, c_3$ are any real numbers.
Statement-$1$: If $c_2$ and $c_3$ are proportional,then $\theta_1 = \theta_2$.
Statement-$2$: $\theta_1 = \theta_2$ for all $c_2$ and $c_3$.