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In the figure, PQ = RS and ∠ORS = 48°. Find ∠OPQ and ∠ROS.

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‘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°

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