Answer:
Step-by-step explanation:
2∠0PQ = 36
∠OPQ = 36/2 = 18°
Join OQ,
ΔOPQ is an isosceles triangle as OP = OQ = radius
∠OQP = ∠OPQ {Angles opposite to equal sides are equal}
∠OQP = 18°
∠ORQ = 36
ΔORQ is an isosceles triangle as OR = OQ = radius
∠OQR = ∠ORQ {Angles opposite to equal sides are equal}
∠OQR = 36°
∠PQR = ∠PQO + ∠OQR
= 18 + 36
∠PQR = 54°
∠POR = 2*∠PQR {Central angle theorem}
= 2 * 54
∠POR = 108°
∠PQR + ∠PSR = 180 {Opposite angles of cyclic quadrilateral}
54 + ∠ PSR = 180
∠PSR = 180 - 54
∠PSR = 126°
∠PSR + ∠RST = 180 {linear pair}
126 + ∠RST = 180
∠RST = 180 - 126
∠RST = 54°
