For the angle 1985°, find the smallest positive angle and the largest negative angle with the same…

Step 1. Whole turns. $1985 = 5 \times 360 + 185$. So $1985^\circ - 5 \times 360^\circ = 185^\circ$, the smallest positive angle.

Step 2. One more turn back. $185^\circ - 360^\circ = -175^\circ$, the largest negative angle.

Step 3. The quadrant. $185^\circ$ lies between $180^\circ$ and $270^\circ$: the third quadrant.