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In the Below Fig, Lines Pq and Rs Intersect Each Other at Point O. If ∠Por: ∠Roq − 5 : 7, Find All the Angles. - Mathematics

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In the below fig, lines PQ and RS intersect each other at point O. If ∠POR: ∠ROQ − 5 : 7,
find all the angles.

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Solution

Given `∠`POR and `∠`ROP is linear pair

`∠`POR + `∠`ROP = 180°

Given that

`∠`POR : `∠`ROP = 5 : 7

∴ `∠`POR =`5/12`×  ´180 = 75°

Similarly `∠`ROQ =   `7/(5+7)` ×180° = 105°

Now, `∠`POS = `∠` ROQ = 105°              [ ∵ Vertically opposite angles]

∴ `∠`SOQ = `∠`POR = 75°                        [ ∵  Vertically opposite angles]

            

Concept: Concept of Parallel Lines
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.2 | Q 16 | Page 16

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