Question

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. Pove that =)

Angle ROS = 1/2(AngleQOS - AnglePOS)​

Answer 1

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Answer 2

Given informations should be written first for these types of questions. After that you have to apply your mind simply like a video player. When a video player is switched on, after that it plays video. In this case, switch on the process in your mind and after that start playing tge process.

Here, the way is somewhat complex but whenever you will observe the solution, it will really become very easy to you. But, for these kinds of questions, the fact is how to solve different questions differently. That is fully dependent on the amount of rapid practice of different problems differently, even from different books. Sometimes, it may also happen, one questions is getting solved differently, i.e., by different processes. At that case, if there is any process which you are feeling easy, accept that process. Thats all for these kinds of numericals.

One more way to do this numerical can be :

∠POR = ∠ROQ = 90°   ( ∵ OR is perpendicular to line PQ)

∠QOS = ∠ROQ + ∠ROS = 90° +∠ROS 

We can write,

∠POS = ∠POR - ∠ROS = 90° -∠ROS   

Now, by further proceeding, we can say :

∠QOS - ∠POS = 90o + ∠ROS – (90° - ∠ROS)

Or, ∠QOS - ∠POS = 90o + ∠ROS – 90° +∠ROS

Or, ∠QOS - ∠POS = 2∠ROS

Or, ∠ROS = 1/2 (∠QOS - ∠POS)