Q. 24.4( 25 Votes )

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

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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