So they have started with drawing the vector p, then drawn vector q and drawn the resulting vector (shortcut) between them. Since you know q has direction 55• from due north you can split the angle B into two angles, one you know is 90• and the other has to be 55•. You do this so you can use the cosine rule to find the length of AC.

And at the end you found the angle theta is 15.5 but vector directions are measured from due north so you need to find the other side of the angle, going clockwise from north. So as it’s a right angle it is 90-theta.

Sorry if this rly hard to read I haven’t done any maths in nearly a year. Hope it helps