1. Let's start by understanding the quadrants. The first quadrant is where angles measure from $0^\circ$ to $90^\circ$, and the fourth quadrant is where angles measure from $270^\circ$ to $360^\circ$. 2. Angles like $165^\circ$ and $195^\circ$ lie in the second and third quadrants respectively, not in the first or fourth quadrants. 3. Therefore, if $x$ is restricted to only the first and fourth quadrants, it cannot be $165^\circ$ or $195^\circ$ because those are outside these quadrants. 4. The confusion usually arises if there's a misunderstanding about the angle measures or if the problem doesn't limit the quadrant for $x$. Make sure to clarify the problem's conditions on the quadrant for $x$.