If m< mnq = 48 degrees and m< nqp = 33 degrees. justify why tiangle qnp must be isocles.

Check the picture below.

an isosceles triangle has two sides that are twins.

if you notice triangle MQN, there are tickmarks on MQ and QN, meaning MQ = QN.  Now both of those twin sides will make twin angles at the base, notice the red colored twin angles.

now, the line MNP is just a flat-line, and a flat-line always is 180°.  At the vertex N, there's one of the twin angles which is 66°, the angle on the other side of the flat-line, is 180° - 66°, therefore 114°.

Since all interior angles in a triangle add up to 180°, the angles at N and Q and P, will be 180°, therefore if we subtract 33° and 114° from 180°, what we'd be left with, is the angle at the vertex P.

Since the angles at Q and P are both twins, the sides that makes them stemming out of N, have to also be twins, and therefore QNP would be an isosceles.

Jim has run 5/6 of a mile so far. i hope that answers your question! good luck : )