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19. In the Below 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 = 1 (∠Qos − ∠Pos). - Mathematics

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In the below fig, POQ is a line. Ray OR is perpendicular to line OS is another ray lying

between rays OP and OR. Prove that ∠ROS = 1 (∠QOS − ∠POS).

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Solution

Given that, OR perpendicular

∴`∠`POR = 90°

`∠`POS + `∠`SOR = 90°                 [∴ `∠`POR = `∠`POS + `∠`SOR]

`∠`ROS = 90° - `∠`POS         ..........(1)

`∠`QOR = 90°           (∴ OR  ⊥ PQ)      

`∠`QOS - `∠`ROS = 90°     

`∠`ROS = `∠`QOS - 90°             .........(2)

By adding (1) and (2) equations, we get

2`∠`ROS = `∠`QOS - `∠`POS

`∠`ROS = `1/2` (`∠`QOS - `∠`POS )

Concept: Introduction to Lines and Angles
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.2 | Q 19 | Page 17
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