Suppose there is a line making an angle $\theta$ with $z$ axis in three dimensions. Then what will be the angles of that line with $x$ and $y$ axes?
You have not provided enough information to answer your question — unless the angle $\theta$ happens to be zero. The set of all lines making some angle $\theta$ with the $z$ axis is a cone centered around the $z$ axis. Different lines making up that cone have different angles with the $x$ and $y$ axes, ranging from $\pi/2 - \theta$ to $\pi/2 + \theta$ (or in degrees, from $90^\circ - \theta$ to $90^\circ + \theta$).
This is true quite generally — not just for angles relative to the axes or just for Cartesian coordinates, but for any angle with respect to any other line and in any coordinate system. There are infinitely many different lines that could have some particular angle relative to any given line, so depending on which of those different lines happens to be your one line, there could be many different answers.