Question

In Fig. 6.17, POQ is a line. Ray OR is perpendicular
to line PQ. OS is another ray lying between rays
OP and OR. Prove that
angle ROS= 1/2 (angle QOS- angle POS).
​

Answer 1

Answer:

Your answer

Step-by-step explanation:

Given:

OR perpendicular to PQ.

\implies \angle ROQ = 90\degree⟹∠ROQ=90°

Proof:

/* From the figure ,

\angle ROS = \angle QOS - \angle QOR \:---(1)∠ROS=∠QOS−∠QOR−−−(1)

\angle ROS = \angle ROP - \angle POS \:---(2)∠ROS=∠ROP−∠POS−−−(2)

/* Adding (1) and (2)

\angle ROS + \angle ROS = \angle QOS - \angle QOR + \angle ROP - \angle POS∠ROS+∠ROS=∠QOS−∠QOR+∠ROP−∠POS

Since , \angle QOR = \angle ROP = 90\degree \:(given)Since,∠QOR=∠ROP=90°(given)

\implies 2\angle ROS = \angle QOS - \angle POS⟹2∠ROS=∠QOS−∠POS

\implies \angle ROS = \frac{1}{2} [\angle QOS - \angle POS ]⟹∠ROS=

2

1

[∠QOS−∠POS]

Hence , proved .Hence,proved.

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