Question

In the given Figure, POQ is a line. Ray OR 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

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)

have a wonderful day ahead

Answer 2

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∠ROS=90°-POS-(i)

∠QOS=∠QOR+∠ROS=90°+/ROS

90⁰ = ∠QOS -∠ROS (ii)

Substituting (ii) in (i) we get

∠ROS =∠QOS -∠ROS -∠POS

2∠ROS =∠QOS - ∠POS

∠ROS = 21(∠QOS - ∠POS)