She should hold the umbrella a little inclined towards the west from the vertical.
The drops which are falling a little ahead of the current position of the woman, will fall on her, because she moves in that direction.
relative velocity of the rain drops wrt cyclist
= velocity of woman - velocity of rain
the magnitude of relative velocity the rain drops wrt woman
= √(122 + 352) = 37 m/s
direction of relative velocity of the rain drops =
= tan-1 (12/35) = 18.92 deg. from the vertical.
So the cyclist should hold the umbrella at 18.92 deg to the vertical in the forward direction.