Adding....?? I don't know what to call it

Question

If angles $ (A+B) \in (90°,270°)$ (sum of these two angles lie in the second and third quadrant) and $(A-B) \in (90°,270°)$, can I say $A \in (90°,270°)$ by adding these two, or is it wrong? In the question, I was given this information and had to find which quadrant does angle $A$ belong to. Please justify your answer.

I tried searching on google but then I didn't know how to put my query in words.

Answer 1

Yes, you can do it as you are proposing. The information is only that $90<A+B<270$ and $90<A-B<270$. Adding this inequalities yields the answer.