The angle between the lines $x \cos 30^\circ + y \sin 30^\circ = 3$ and $x \cos 60^\circ + y \sin 60^\circ = 5$ is .....$^\circ$

The acute angle between the lines $x \cos 30^{\circ} + y \sin 30^{\circ} = 3$ and $x \cos 60^{\circ} + y \sin 60^{\circ} = 5$ is (in $^{\circ}$)

Find the equation of the line passing through the point $(4, 5)$ and making equal angles with the lines $3x = 4y + 7$ and $5y = 12x + 6$.

Find the angles between the lines $\sqrt{3}x + y = 1$ and $x + \sqrt{3}y = 1$.

Two equal sides of an isosceles triangle are along $-x+2y=4$ and $x+y=4$. If $m$ is the slope of its third side,then the sum of all possible distinct values of $m$ is:

If the equation of a line having a slope $m$ $(m \in \mathbb{Z})$,passing through $(1, 1)$ and making an angle of $\tan^{-1}\left(\frac{5}{7}\right)$ with the line $x + y - 3 = 0$ is $ax + y + c = 0$,then $ac =$