In the figure, lines $p$ and $q$ are parallel, and line $t$ is a transversal. The angle $x^{\circ }$ is an interior angle in the upper-right position relative to line $p$ and line $t$. The angle $y^{\circ }$ is an exterior angle in the lower-left position relative to line $q$ and line $t$. What is the value of $x+y$?

(Note: The figure shows two parallel lines $p$ and $q$ intersected by a transversal $t$. Angle $x^{\circ }$ is between line $p$ and $q$ and to the right of $t$. Angle $y^{\circ }$ is below line $q$ and to the left of $t$.)