Question

Plz answer the given question.
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Answer 1

Answer:

Given that,

POQ is a line, ∠POR = 90°

Lets construct OT such that, ∠ROT = ∠ROS

⇒∠ROS + ∠ROT = 2 ∠ROS → Equation (i)

Since both angles are equal.

[ please see the attachment for clarity ]

So,

∠POR - ∠SOR = ∠QOR - ∠ROT

⇒∠POS = ∠QOT

∠ROS is also equal to ∠QOS - ∠QOR → Equation (ii)

Now, ∠QOR = ∠ROT + ∠QOT

⇒ ∠QOR = ∠ROT + ∠POS [∠POS = ∠QOT ]

Substituting ∠QOR = ∠ROT + ∠POS in Equation(ii), we get

∠ROS = ∠QOS - (∠ROT + ∠POS )

⇒ ∠ROS = ∠QOS - ∠ROT - ∠POS

⇒ ∠ROS + ∠ROT = ∠QOS - ∠POS

⇒ 2 ∠ROS = ∠QOS - ∠POS

⇒ ∠ROS = 1/2 [∠QOS - ∠POS ]

Hence proved

Answer 2

Step-by-step explanation:

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