Question: In the given figure, if the line segment $PQ$ is parallel to the line segment $RS$, find the value of $y$.
1. **State the problem:** We are given a quadrilateral with points $P$, $Q$, $R$, and $S$ where $PQ \parallel RS$. We need to find the value of $y$ based on the given angle relationships.
2. **Identify the angles and relationships:** Since $PQ \parallel RS$, the interior angles on the same side of the transversal $QS$ are supplementary.
3. **Write the equation for supplementary angles:** The angles at $Q$ and $S$ along $QS$ add up to $180^\circ$.
4. **Express the angles at $Q$:** At $Q$, the two interior rays form angles $y$ and $5y$, so the total angle at $Q$ is $$y + 5y = 6y.$$
5. **Express the angle at $S$:** The angle at $S$ between $QS$ and $RS$ is given as $11y$.
6. **Set up the supplementary angle equation:**
$$6y + 11y = 180$$
7. **Simplify and solve for $y$:**
$$17y = 180$$
$$y = \frac{180}{17}$$
8. **Final answer:**
$$y = \frac{180}{17} \approx 10.59$$ degrees.
This means the value of $y$ is approximately $10.59$ degrees.