In $\triangle ABC$, $\angle A = 100^\circ$, $\angle B = 50^\circ$, $\angle C = 30^\circ$, $\overline{AH}$ is an altitude, and $\overline{BM}$ is a median. Then $\angle MHC=$

$\textrm{(A)}\ 15^\circ\qquad\textrm{(B)}\ 22.5^\circ\qquad\textrm{(C)}\ 30^\circ\qquad\textrm{(D)}\ 40^\circ\qquad\textrm{(E)}\ 45^\circ$
We are told that $\overline{BM}$ is a median, so $\overline{AM}=\overline{MC}$. Drop an altitude from $M$ to $\overline{HC}$, adding point $N$, and you can see that $\triangle ACH$ and $\triangle MCN$ are similar, implying $\overline{HN}=\overline{NC}$, implying that $\triangle MNH$ and $\triangle MNC$ are congruent, so $\angle MHC=\angle C=30^\circ$.