how do you determine the direction angle for the vector sum problems?

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You can find the x and y component vectors for each vector, and adding them would give the x and y components of the final vector. The direction here can be given by tan^-1(y/x) where y is the y-component vector for the final vector and x is the x-component vector. It's kind of hard to put it in words but I hope this helps. Example: Vector 1: 4x+2y Vector 2: 5x-6y Final vector: 9x-4y Direction of final vector: tan^-1(-4/9)=-23.96deg