Since s is positive, s+35° is positive, so you can get a positive co-terminal
angle by adding 360°, so s+35°+ 360° or s+395° is an answer to the first
question.
Unless you are given the value of s, there is no way to be sure that you have
subtracted 360° enough times to get a negative co-terminal angle. For instance,
suppose s were equal to 100000000000000°. Then s+35° would be 100000000000035°,
and you'd have to subtract 360° many, many times to get a negative coterminal
angle. So there is no way to answer your second question, without knowing
anything about how large s is.
Edwin