Question

Class 9 Chapter -6 (Lines and Angles) Exercise- 6.1 Que no. 5th 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 ?​

Answer 1

Answer:

ray 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 = 12(∠QOS−∠POS)

Answer 2

Answer:

Here is the solution in the attachment.

Hope it helps you