1. **Problem statement:** We are given a quadrilateral with interior angles labeled $x$, $y$, $z$, and $w$. We need to find the value of $x + y + z + w$. 2. **Formula and rule:** The sum of the interior angles of any quadrilateral is always $360^\circ$. This is a fundamental property of quadrilaterals. 3. **Applying the rule:** Since $x$, $y$, $z$, and $w$ are the interior angles of the quadrilateral, we have: $$x + y + z + w = 360$$ 4. **Conclusion:** Therefore, the value of $x + y + z + w$ is $360$ degrees. This holds true regardless of the shape of the quadrilateral as long as it is a simple polygon with four sides.