Problem: <image>In $\Delta G H J$, $H P=5 x-16$, $P J=3 x+8$, $m \angle G J N=6 y-3$, $m \angle N J H=4 y+23$ and $m \angle H M G=4 z+14$. If $\overline{HM}$ is an altitude of $∠GHJ$, find the value of $z$.
Answer: 19