The bisector $PQ$ of segment $MN$ at point $Q$ with $\angle PQN = 45^\circ$ and $MN = 7$ cm gives $MQ$ equal to—

A perpendicular bisector divides the segment into two equal halves at $Q$, so $MQ = \tfrac{1}{2}MN = \tfrac{1}{2}\times 7 = 3.5$ cm. The given angle does not affect the bisected length.