For example a.
fx = 15*cos(65°) + 37*cos(142°) so fx = --22.817
fy = 15*sin(65°) + 37*sin(142°) so fy = 36.374
f = sqrt((-22.817)^2 + 36.374^2) so f = 42.938
Angle theta = tan-1(fy/fx) = tan-1(36.374/-22.817) = -57.9° However, because fy is positive and fx is negative this is in the second quadrant, so the angle from the positive x-direction going anti-clockwise around to the resulatnt is 180°-57.9° = 122.1°