In the diagram, |PQ| = |PR| = |RS| and ∠RPS = 32°. Find ∠QPR.

Given that $|PR| = |RS|$, $\triangle PRS$ is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal.
Therefore, $\angle RSP = \angle RPS$.
Since $\angle RPS = 32^\circ$, then $\angle RSP = 32^\circ$.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Given that $|PQ| = |PR|$, $\triangle PQR$ is an isosceles triangle.
Therefore, $\angle PQR = \angle PRQ$.
From Step 2, we found $\angle PRQ = 64^\circ$.
So, $\angle PQR = 64^\circ$.

The sum of angles in a triangle is $180^\circ$.

The value of $\angle QPR$ is $52^\circ$.

The correct option is D.

$\boxed{\text{D. } 52^\circ}$