Prove that the bisector of one angle of a pair of vertically opposite angles when produced backwards bisect the other angles of the pair .

Question

Prove that the bisector of one angle of a pair of vertically opposite angles when produced backwards bisect the other angles of the pair .

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Jasmine 4 weeks 2021-08-16T05:13:55+00:00 1 Answer 0 views 0

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    2021-08-16T05:15:22+00:00

    Answer:

    AB and CD are straight lines intersecting at O.

    OX the bisector of ∠AOC and OY is the bisector of ∠BOD

    OY is the bisector of ∠BOD

    ∠1=∠6….(i)

    OX is the bisector of ∠AOC

    ∠3=∠4…..(ii)

    ∠2=∠5…..(iii) [vertically opposite angle]

    Sum of all angles =360  

    o

     

    ∠1+∠2+∠3+∠4+∠5+∠6=360  

    o

     

    ⇒∠1+∠2+∠3+∠3+∠2+∠1=360  

    o

     

    2∠1+2∠2+2∠3=360  

    o

     

    ⇒∠DOY+∠AOD+∠AOX=180  

    o

     

    ∠XOY=180  

    o

     

    Step-by-step explanation:

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