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.
