In quadrilateral P QRS, diagonals P R and SQ intersect at O inside P QRS, SP = SQ = SR = 1, and
∠QSR = 2∠QSP. Marc determines the measure of
the twelve angles that are the interior angles of 4P OS,
4P OQ, 4ROS, and 4ROQ. The measure of each of
these angles, in degrees, is a positive integer, and exactly
six of these integers are prime numbers. How many
different quadrilaterals have these properties and are not
rotations or translations of each other?