Question

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Answer 1

Answer:

For the solution see the attachment.

Hope it helps you

Answer 2

Given: POQ is a line and OR is perpendicular to PQ. OS is another day between OP and OR.

Prove: ∠ROS = 1/2 (∠QOS−∠POS)

Solution:

OP⊥ PQ _____ (GIVEN)

*Refer the Attachment for figure.

As, we can easily see in fig. ∠ROQ = 90°

Similarly,

∠ROP = 90°

From above it's clear that..

∠ROQ = ∠ROP (As both are 90°)

Now..

→  ∠POS + ∠SOR = ∠ROQ

→  ∠POS + ∠ROS = ∠QOS - ∠ROS

→  ∠ROS + ∠ROS = ∠QOS + ∠POS

→ 2∠ROS = ∠QOS + ∠POS

→  ∠ROS = 1/2 (∠QOS + ∠POS)

________ [ PROVED ]

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