Question 5In Fig. POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that∠ROS = 12\dfrac{1}{2}21 (∠QOS – ∠POS).

Question

Question 5In Fig. POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that∠ROS = 12\dfrac{1}{2}21​ (∠QOS – ∠POS).

Accepted Answer

Since, OR ⊥ PQ∴ ∠ROP = 90° and ∠ROQ = 90°∴ ∠ROS = 90° - ∠POS .......(1)⇒ ∠QOS = ∠QOR + ∠ROS⇒ ∠QOS = 90° + ∠ROS⇒ 90° = ∠QOS - ∠ROS .....(2)Substituting value of 90° from equation (2) in equation (1), we get :⇒ ∠ROS = (∠QOS - ∠ROS) - ∠POS⇒ ∠ROS + ∠ROS = ∠QOS - ∠POS⇒ 2(∠ROS) = ∠QOS - ∠POS⇒ ∠ROS = 12\dfrac{1}{2}21​ (∠QOS - ∠POS)Hence, proved ∠ROS = 12\dfrac{1}{2}21​ (∠QOS - ∠POS).

Lines and Angles — Question 5

Question 5