1. Statement of the problem: The relation between the sum $y$ of the interior angles of a polygon and the number of its sides $x$ is given by the formula below. $$y = \pi(x - 2)$$. 2. Formula interpretation: Here $x$ represents the number of sides of a polygon and $y$ is the sum of its interior angles. 3. Important rule: The number of sides of a polygon must be a positive integer and at least 3 because a polygon has a minimum of three sides. 4. Therefore $x\in$ $\mathbb{Z}^+$ and $x\ge 3$. 5. Intermediate evaluation: For $x=3$ we get $y=\pi(3-2)=\pi$ and for $x=4$ we get $y=\pi(4-2)=2\pi$ which shows the formula produces valid angle sums for integer $x\ge 3$. 6. Conclusion: The domain is $\mathbb{Z}^+ \setminus \{1,2\}$ which corresponds to choice (d). Final answer: (d) $\mathbb{Z}^+ \setminus \{1,2\}$.