Question

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Answer 1

Step-by-step explanation:

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Answer 2

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

Prove: $\angle{ROS}$ = 1/2 $(\angle{QOS}\:-\:\angle{POS}$

Solution:

OP $\perp$ PQ _____ (GIVEN)

*Refer the Attachment for figure.

As, we can easily see in fig. $\angle{ROQ}$ = 90°

Similarly,

$\angle{ROP}$ = 90°

From above it's clear that..

$\angle{ROQ}$ = $\angle{ROP}$ (As both are 90°)

Now..

→ $\angle{POS}$ + $\angle{SOR}$ = $\angle{ROQ}$

→ $\angle{POS}$ + $\angle{ROS}$ = $\angle{QOS}$ - $\angle{ROS}$

→ $\angle{ROS}$ + $\angle{ROS}$ = $\angle{QOS}$ + $\angle{POS}$

→ 2$\angle{ROS}$ = $\angle{QOS}$ + $\angle{POS}$

→ $\angle{ROS}$ = 1/2$(\angle{QOS}$ + $\angle{POS})$

________ [ PROVED ]

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