Based on the provided image, the lines PQ and RS are parallel. We are given three angles: $x$ at point $Q$, $y$ at point $R$, and $z$ at the point between $Q$ and $R$. We need to find a relationship between $x$, $y$, and $z$.

1. Problem Description

Based on the provided image, the lines PQ and RS are parallel. We are given three angles: $x$ at point $Q$, $y$ at point $R$, and $z$ at the point between $Q$ and $R$. We need to find a relationship between $x$, $y$, and $z$.

2. Solution Steps

Since line PQ is parallel to line RS, we can draw a line through the vertex of angle $z$ such that this line is parallel to PQ and RS. Let us call the angles formed as a result of drawing the parallel line as $a$ and $b$, where $a$ is between the line QR and the newly drawn parallel line, and $b$ is between the line RQ and the newly drawn parallel line. Then, $a + b = z$.

Since PQ and the new line are parallel, $x$ and $a$ are alternate interior angles, so $x = a$.

Since RS and the new line are parallel, $y$ and $b$ are alternate interior angles, so $y = b$.

Therefore, $z = a + b = x + y$.

3. Final Answer

$z = x + y$