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To find the measure of angle \(\angle RPS\), you can use the fact that the sum of angles in a triangle is \(180^\circ\).

Given:

• \(\angle PTR = 71^\circ\)

Since \(\triangle PTR\) is a right triangle (as indicated by the square at point \(T\)), \(\angle PRT = 90^\circ\).

The sum of angles in a triangle is: \[ \angle PTR + \angle PRT + \angle RPS = 180^\circ \]

Substitute the known values: \[ 71^\circ + 90^\circ + \angle RPS = 180^\circ \]

Calculate \(\angle RPS\): \[ \angle RPS = 180^\circ - 71^\circ - 90^\circ = 19^\circ \]

Thus, \(\angle RPS\) measures \(19^\circ\).