The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is

Find the angle between the lines $y - \sqrt{3}x - 5 = 0$ and $\sqrt{3}y - x + 6 = 0$. (in $^{\circ}$)

$A$ straight line through the point $(3, -2)$ is inclined at an angle $60^{\circ}$ to the line $\sqrt{3}x + y = 1$. If it intersects the $X$-axis, then its equation will be

If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{\pi}{4}$ at the origin,then the absolute value of the product of all possible values of $a$ is:

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

$A$ straight line through the origin bisects the line segment joining the points $(a \cos \alpha, a \sin \alpha)$ and $(a \cos \beta, a \sin \beta)$. Then the lines are