Question 5. In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another Chapter 6: Lines and Angles Maths Class 9 solutions are developed for assisting understudies with working on their score and increase knowledge of the subjects. Question 5. 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. Prove that ∠ ROS = 1/2(∠ QOS – ∠ POS). is solved by our expert teachers. You can get ncert solutions and notes for class 9 chapter 6 absolutely free. NCERT Solutions for class 9 Maths Chapter 6: Lines and Angles is very essencial for getting good marks in CBSE Board examinations
Question 5. 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. Prove that ∠ ROS = 1/2(∠ QOS – ∠ POS).
Solution
It is given that OR is perpendicular to PQ
So that ∠POR = 90°
sum of angle in linear pair always equal to 180°
∠POS + ∠SOR + ∠POR = 180°
Plug ∠POR = 90°
90°+∠SOR + ∠POR = 180°
∠SOR + ∠POR = 90°
∠ROS = 90° − ∠POS … (1)
∠QOR = 90°
Given that OS is another ray lying between rays
OP and OR so that
∠QOS − ∠ROS = 90°
∠ROS = ∠QOS − 90° … (2)
On adding equations (1) and (2), we obtain
2 ∠ROS = ∠QOS − ∠POS
∠ROS = 1/2(∠QOS − ∠POS)
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