Question 9$M$ and $N$ are midpoints of $AD$ and $AB$, respectively, in rectangle $ABCD$. Lines $BM$ and $DN$ intersect at point $P$. Find $\angle MPD$, given that $\angle MBC=\angle BCN+31^\circ$. $23^\circ$$31^\circ$$38^\circ$$42^\circ$None of the above