To find \( m \angle OPS \), we can use the information given about the angles and the parallel lines.
Since \( OQ \) and \( RT \) are parallel lines, we know that the angles formed by a transversal line with these parallel lines follow certain properties.
In this case, \( \angle QPS \) and \( \angle OPS \) are alternate interior angles. Therefore, they are equal when the lines are crossed by a transversal.
Given that \( m \angle QPS = 67^\circ \), we have:
\[ m \angle OPS = m \angle QPS = 67^\circ \]
Hence, the measure of angle \( OPS \) is:
\[ \boxed{67^\circ} \]