Q. 24.4( 25 Votes )
In the figure, PQ = RS and ∠ORS = 48°. Find ∠OPQ and ∠ROS.
Answer :
In 
ORS,
∠ORS = ∠OSR (radius of circle)
∠OSR = ∠ORS = 480
∠OSR + ∠ORS + ∠ROS = 180
⇒ 48
+ 48
+ ∠ROS = 180
⇒ 96
+ ∠ROS = 180
⇒ ∠ROS = 180
-96
⇒ ∠ROS = 180
-96
⇒ ∠ROS = 84
We know “Angles subtended by equal chords at the center of a circle are equal”.
∠POQ = ∠ROS = 840
In 
POQ,
∠POQ + ∠OPQ + ∠OQP = 180
840 + x + x = 180
840 + 2x = 180
2x = 180
-84
2x = 96
x = 
x = 48
∠OPQ = 48
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