The diagonals $PR$ and $QS$ of the rhombus intersect each other at the point $O$. What is the value of $\angle POS$?

A fundamental property of a rhombus is that its diagonals bisect each other at right angles ($90^{\circ }$). Since $PR$ and $QS$ are the diagonals intersecting at $O$, the angle between them ($\angle POS$) must equal $90^{\circ }$.