Show that two intersecting lines form a pair of vertically opposite angles.
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:
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
Answer:
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Step-by-step explanation:
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