We are given a diagram with parallel lines and a triangle. We are asked to find the relationship between the angles $x$, $y$, and $z$.

1. Problem Description

We are given a diagram with parallel lines and a triangle. We are asked to find the relationship between the angles $x$, $y$, and $z$.

2. Solution Steps

Let's denote the line segment by their endpoints. Line segment $PQ$ is parallel to line segment $RS$. Let the angle at vertex $Q$ be $x$, the angle at vertex $R$ be $y$, and the angle at vertex $Z$ be $z$.

Since $PQ$ is parallel to $RS$, the angle between $QR$ and $RS$ is equal to the angle between $PQ$ and $QR$. This angle is the alternate interior angle and is $x$.

In triangle $QRZ$, the sum of angles in a triangle is $180^{\circ}$.

Therefore, $x+y+z = 180^{\circ}$.

3. Final Answer

$x+y+z = 180^{\circ}$