If two planes are intersected by making a straight line, like $AB$ then
Does the angle between two planes (see figure) always given by the angle between normal vectors ($n_1$ and $n_2$) ?
Yes. See here
It[The angle between two planes] is defined as the angle between 2 lines, one in each plane, so that they are at right angles to the line of intersection of the 2 planes (like the angle between the tops of the pages of an open book).
To find this angle, will we first have to find the equation of the line of intersection of the 2 planes, and then find 2 vectors which are in the planes and perpendicular to this? Fortunately no! We just need to know a normal vector to each of the planes.