A = Axi + Ayj
B = Bxi + Byj
Where i = unit vector in the x direction and j = unit vector in the y direction. The x and y components of vectors A and B are given by:
Ax = A*cosθA
Ay = A*sinθA
Bx = B*cosθB
By = A*sinθB
A + B = (Ax+Bx)i + (Ay+By)j
Plug in the values for A, B, θA and θB to get the answer.