Question

In the given figure POQ ios a line. OR ⊥ PQ. OS is another ray lying between rays OP

and OR. Prove that ∠ROS = 1/2

(∠QOS – ∠POS) ​

Answer 1

Answer:

In the question, it is given that (OR ⊥ PQ) and POQ = 180°

So, POS+ROS+ROQ = 180°

Now, POS+ROS = 180°- 90° (Since POR = ROQ = 90°)

∴ POS + ROS = 90°

Now, QOS = ROQ+ROS

It is given that ROQ = 90°,

∴ QOS = 90° +ROS

Or, QOS – ROS = 90°

As POS + ROS = 90° and QOS – ROS = 90°, we get

POS + ROS = QOS – ROS

2 ROS + POS = QOS

Or, ROS = ½ (QOS – POS) (Hence proved).

Answer 2

Answer:

Step-by-step explanation:

∠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=21​(∠QOS−∠POS)

Hence proved.