Point O is the center of the circle on which points P, Q and R lie in such a way that OPQR is a rhombus. Find the ORQ angle.

Note that OPQR is a rhombus, so OP = PQ = QR = RO = r, where r is the radius of the circle. Also, the angles ORQ and OPQ, ROP and RQP are equal. Let’s draw a segment ОQ. Q lies on a circle, O is its center. Therefore, OQ = r. Note: OQ = r = OR = RQ, which means that the ORQ triangle is equilateral, therefore all the angles of this triangle are 60 ° => the ORQ angle is 60 °.
Answer: 60 °.