If you have some angle $X$ (assuming degrees), and you have to find its measure that is in interval $[0, 360)$, then the following might help:
If $X$ is any angle, and if we ignore multiple turns, then there is a corresponding angle that is in $[0,360)$. When we're talking about angles, then following holds $X = X + 360k, k\in \mathbb{Z}$, if we ignore the turns. In your case we have $-90 + 360k, k = 0$, choose $k=1$ and get $-90+360=270$.
More generally: Let $X$ be some angle in degrees. Then if we ignore multiple turns, its corresponding angle $X'$ in $[0, 360)$ is determined by following formula: $$ X' = X - \lfloor X/360 \rfloor \cdot 360 $$