GAUSS8 2019 Problem 25

In quadrilateral P Q R S, diagonals P R and S Q intersect at O inside P Q R S, S P=S Q=S R=1, and \angle Q S R=2 \angle Q S P. Marc determines the measure of the twelve angles that are the interior angles of \triangle P O S, \triangle P O Q, \triangle R O S, and \triangle R O Q. 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?

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Answer Choices
A. 7
B. 5
C. 9
D. 6
E. 8