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Ab, Cd and Ef Are Three Concurrent Lines Passing Through the Point O Such that of Bisects ∠Bod. If ∠Bof = 35°, Find ∠Boc and ∠Aod. - Mathematics

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AB, CD and EF are three concurrent lines passing through the point O such that OF bisects
∠BOD. If ∠BOF = 35°, find ∠BOC and ∠AOD.

 

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Solution

Given

OF bisects  `∠`BOD

OF bisects  `∠`BOD

`∠`BOF = 35°

`∠`BOC = ?

`∠`AOD = ?

∴`∠`BOD = 2 `∠`BOF = 70°                    [ ∵ of bisects `∠`BOD]

  `∠`BOD = `∠`AOC = 70°              [ `∠`BODand `∠`AOCare vertically opposite angles]

Now,

      `∠`BOC + `∠`AOC = 180°

⇒ `∠`BOC + 70° = 180°

⇒`∠`BOC = 110°

∴ `∠`AOD = `∠`BOC = 110°               [Vertically opposite angles]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Concept: Pairs of Angles
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.3 | Q 8 | Page 23

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