How do they conclude that the anle is 30^o?
Try drawing the reciprocal and real space lattice vectors and computing the angle from knowing the angle between the reciprocal ones from the one in real space ones.
How can I draw the reciprical lattice vectors before I have calculated them?
Use that they are orthogonal to all the other real space vectors. There’s only one direction in 2D that is orthogonal to a given vector.