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

If the line through the points $(-2, 6)$ and $(4, 8)$ is perpendicular to the line passing through the points $(8, 12)$ and $(x, 24)$,then the value of $x$ is

If the straight line $2x - 3y + 17 = 0$ is perpendicular to the line passing through the points $(7, 17)$ and $(15, \beta)$,then $\beta$ equals:

If $A (-2, 1)$,$B (2, 3)$,and $C (-2, -4)$ are three points,then what is the angle between $BA$ and $BC$?

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

The equation of the lines which pass through the point $(3, -2)$ and are inclined at $60^o$ to the line $\sqrt{3}x + y = 1$ is: