Is there a recursive formula for adding vectors based on their angle to find their position?

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Given X amount of vectors, and their respective angle and length, how can I find the respective position? I have uploaded an image example for reference

[example using 4 vectors] ab length = 4 bc length = 8 cd length = 16 de length = 8

NOTE: the angle is the angle at which the following vector is shifting from its previous point. angle b = 20 angle c = 0 angle d = 270

enter image description here