‘O’ is the centre of the circle.
PQ = RS [given, equal chords]
∴∠POQ = ∠ROS [ ∵ equal chords make equal angles at the centre]
∴ In ΔROS ∠ORS + ∠OSR + ∠ROS = 180°
[angle sum property]
∴ 48° + 48° + ∠ROS = 180°
[ ∵ OR = OS(radii); ΔORS is isosceles]
∴ ∠ROS = 180° – 96° = 84°
Also ∠POQ = ∠ROS = 84°
∴ ∠OPQ = ∠OQP
[∵ OP = OQ; radii]
= 1/2 [180°-84°] = 48°