The acute angle between the lines $x-y=0$ and $y=0$ is

$A$ straight line $(\sqrt{3} - 1)x = (\sqrt{3} + 1)y$ makes an angle of $75^{\circ}$ with another straight line which passes through the origin. Then the equation of the line is:

Find the acute angle between the lines $y = 3$ and $y = \sqrt{3}x + 9$. (in $^{\circ}$)

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 $c_3$.

Two lines pass through the point $(2,3)$ and intersect each other at an angle of $60^{\circ}$. If the slope of one line is $2$,find the equations of the other line.

The angle between the two lines $y - 2x = 9$ and $x + 2y = -7$ is .....$^o$.