Answer
$\angle$PNQ=45$^{\circ}$
Work Step by Step
$\frac{NP}{MN}$=$\frac{PQ}{MQ}$
$\frac{4}{8}$=$\frac{3}{6}$
$\frac{1}{2}$=$\frac{1}{2}$
QN bisects angle N because the corresponding segments of the triangle are proportional
$\angle$N=180-$\angle$M-$\angle$P
$\angle$N=180-63-27
$\angle$N=90
2$\angle$PNQ=$\angle$N
2$\angle$PNQ=90
$\angle$PNQ=45
