Question

In the given figure, if OP , OQ , OR and OS are the rays such that POQ = ROS = 130 , QOR = POS = 50 . Is it true that POR and QOS are straight lines ? Justify your answer.​

Answer 1

Answer:

∠ROS=90

∘

−∠POS−(i)

∠QOS=∠QOR+∠ROS=90

∘

+∠ROS

⇒90

∘

=∠QOS−∠ROS−(ii)

Substituting (ii) in (i) we get

∠ROS=∠QOS−∠ROS−∠POS

⇒2∠ROS=∠QOS−∠POS

⇒∠ROS=

2

1

(∠QOS−∠POS)

Hence proved.