## 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

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## Answers ( )

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: