To find the measure of \(\angle MRS\), we can use the property of angle bisectors. The angle bisector divides the angle into two equal parts.
Given that \(\angle QRM\) is \(55^\circ\), we know that since \(M\) is on the angle bisector of \(\angle QRS\):
\[ \angle QRM = \angle MRS = 55^\circ \]
Since we want the measure of \(\angle MRS\) and we have assigned that measure directly, we see that the statement is consistent with the information provided.
Thus,
The measure of \(\angle MRS\) is \(55^\circ\).
The correct answer is: The measure of ∠MRS is 55°.