Question

prove that the bisectors of a pair of vertically opposite angles lie on the same straight line​

Answer 1

Answer:

OX is the bisector of ∠AOC

∴∠3=∠4 …….(2)

∠2=∠5 ……….(3) (vertically opposite angles)

We know that, the sum of the angles formed at a point is 360

o

.

∴∠1+∠2+∠3+∠4+∠5+∠6=360

o

⇒∠1+∠2+∠3+∠3+∠2+∠1=360

o

(using 1,2 and 3)

⇒2∠1+2∠2+2∠3=360

o

2(∠1+∠2+∠3)=360

o

⇒∠DOY+∠AOD+∠AOX=180

o

∠XOY=180

o

∴ The bisectors of pair of vertically opposite angles are on the same straight line.