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Question
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]
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