I am working out how to solve for angles during vectors problems, and the only way I can solve for the angles is by trying all possibilities and seeing which ones is the most realistic way of solving for it. So are there any patterns or laws that one can know for knowing which angle to use to subtract it from 180^o? The problem that got me guessing is below:

6.Each of three brothers has tied a rope to a buoy floating on a lake. Paco pulls towards the east with a force of 40 N. Louis pills towards the southwest with a force of 30 N. What forces should Pepe exert to hold his brothers' efforts in equilibrium?

The answer is 28.3 N at 131^o. If you draw a diagram the angle that you need to use to subtract from 180^o is between the 40 N force and the 28.3 N force.