Question

In the figure, PQ=RS and angle ORS= 48
Find angle OPQ and angle ROS.​

Answer 1

Answer:

∠OPQ = 48°

∠ROS = 84°

Step-by-step explanation:

Given: PQ=RS ; ∠ORS=48°

In ΔOPQ and ΔORS,

OP = OR         {radius of circle}

OQ = OS         {radius of circle}

PQ = RS          {given}

∴ By SSS congruence, ΔOPQ ≅ ΔORS

⇒ By CPCT, ∠OPQ = ∠ORS

⇒ ∠OPQ = 48°

w.k.t., opposite angles to equal sides of a triangle are also equal.

∵ OR = OS = radius of circle.

∴ ∠ORS = OSR = 48°

w.k.t., sum of all angles of a triangle is 180°.

⇒ ∠ROS + ∠ORS + ∠OSR = 180°

or ∠ROS + 48° + 48° = 180°

or ∠ROS = 180°-96°

or ∠ROS = 84°

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Answer 2

Step-by-step explanation:

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Is the Answer