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https://docs.godotengine.org/en/3.1/classes/class_vector2.html#class-vector2-method-angle-to
you might wanna change the angle value returned from that funnction to Degrees using...
http://docs.godotengine.org/en/latest/classes/class_@gdscript.html?highlight=rad2deg#class-gdscript-method-rad2deg
then use that angle value to choose which sprite to set...
if angle > 45 and angle < 134:
sprite.set_texture(texUP)
elif angle >= 135 and angle < 224:
sprite.set_texture(texLEFT)
elif angle >= 225 and angle < 314:
sprite.set_texture(texDOWN)
elif angle >= 315 and angle <= 360:
sprite.set_texture(texRIGHT)
elif angle >= 0 and angle <=44
sprite.set_texture(texRIGHT)