Question

Answer this immediately..... ​

Answer 1

Step-by-step explanation:

▪️POQ is a straight line. [Given]

▪️∴ ∠POS + ∠ROS + ∠ROQ = 180°

▪️But OR ⊥ PQ

▪️∴ ∠ROQ = 90°

▪️⇒ ∠POS + ∠ROS + 90° = 180°

▪️⇒ ∠POS + ∠ROS = 90°

▪️⇒ ∠ROS = 90° – ∠POS … (1)

▪️Now, we have ∠ROS + ∠ROQ = ∠QOS

▪️⇒ ∠ROS + 90° = ∠QOS

▪️⇒ ∠ROS = ∠QOS – 90° ……(2)

▪️Adding (1) and (2), we have

▪️2 ∠ROS = (∠QOS – ∠POS)

▪️∴ ∠ROS = (Angel QOS - Angle POS)

Hopes it help you✌️✌️

Answer 2

ANSWER ::

∠ROS=90° −∠POS - - - - - - - - - - (i)

So

∠QOS=∠QOR+∠ROS=90° +∠ROS

⇒90 ° =∠QOS−∠ROS - - - - - - - -- (ii)

Substituting (ii) in (i) we get

∠ROS=∠QOS−∠ROS−∠POS

⇒2∠ROS=∠QOS−∠POS

⇒∠ROS= 1/2 (∠QOS−∠POS)

HENCE THE PROOF FOLLOWS