Mathematics, 04.05.2021 03:41
5. In quadrilateral P QRS, diagonals P R and SQ intersect at O inside PQRS, SP = SQ = SR = 1, and ∠QS R = 2∠QS P . Marc determines the measure of the twelve angles that are the interior angles of △POS, △POQ, △ROS, and △ROQ. 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?