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 = 48^{0}

∠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 = 84^{0}

In POQ,

∠POQ + ∠OPQ + ∠OQP = 180

84^{0} + x + x = 180

84^{0} + 2x = 180

2x = 180-84

2x = 96

x =

x = 48

∠OPQ = 48

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