If $S_1$ and $S_2$ are two straight lines such that the reflection of $S_1$ in $S_2$ and the reflection of $S_2$ in $S_1$ coincide,the angle between $S_1$ and $S_2$ is equal to?

The angle between the lines $x = 2$ and $x - 3y = 6$ is

If a straight line $L$ passing through the point $(5, -3)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x + y - 9 = 0$ and $L$ intersects the $X$-axis,then the equation of $L$ is

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

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 $c_3$.

The angle $\theta$ between the lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ is given by: