PQRS is a rectangle and STUV is a square. Find $\angle\text{PSU}$.

1. Find angle VSP using the right angle of the rectangle

Since PQRS is a rectangle, $\angle PSR = 90^\circ$.
$\angle VSP = \angle PSR - \angle VSR = 90^\circ - 31^\circ = 59^\circ$.

2. Find angle USV using the property of the diagonal of a square

Since STUV is a square, the diagonal SU bisects the right angle $\angle TSV$.
$\angle USV = 90^\circ \div 2 = 45^\circ$.

3. Find angle PSU

$\angle PSU = \angle VSP - \angle USV = 59^\circ - 45^\circ = 14^\circ$.