In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (their sum is \(180^\circ\)).
Given the angles:
- Let's assume \(\angle R = z + 60^\circ\)
- \(\angle S = z\)
Since R and S are consecutive angles, we can write the equation:
\[ (z + 60^\circ) + z = 180^\circ \]
Now, combine like terms:
\[ 2z + 60^\circ = 180^\circ \]
Next, subtract \(60^\circ\) from both sides:
\[ 2z = 120^\circ \]
Now, divide by 2:
\[ z = 60^\circ \]
So the value of \(z\) in the parallelogram RSTU is \(60^\circ\).