Given that line segment PQ is parallel to line segment RS, and the measures of angle PQR is $x$ and angle QRS is $y$. We are asked to find the value of $x+y$.

1. Problem Description

Given that line segment PQ is parallel to line segment RS, and the measures of angle PQR is $x$ and angle QRS is $y$. We are asked to find the value of $x+y$.

2. Solution Steps

Since PQ is parallel to RS, we know that $\angle PQR$ and $\angle QRS$ are interior angles on the same side of the transversal QR.

When two parallel lines are cut by a transversal, interior angles on the same side of the transversal are supplementary. Supplementary angles add up to 180 degrees. Therefore, we have:

$x + y = 180^\circ$

3. Final Answer

$x+y = 180^\circ$