Question

POQ is a line. Ray 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:

From the figure

∠ROS+90

∘

=∠QOS⟹90

∘

=∠QOS−∠ROS

∠QOS+∠POS=180

∘

=2(90

∘

)

∠QOS+∠POS=2∠QOS−2∠ROS

⟹2∠ROS=∠QOS−∠POS

⟹∠ROS=

2

1

(∠QOS−∠POS)

Answer 2

$here \: is \: your \: answer$

___________________________________

From The figure

∠ROS+90∘=∠QOS⟹90∘=∠QOS−∠ROS

∠QOS+∠POS=180∘=2(90∘)

∠QOS+∠POS=2∠QOS−2∠ROS

⟹2∠ROS=∠QOS−∠POS

⟹∠ROS=21(∠QOS−∠POS)

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