Question

Prove that the bisectors of a pair of vertically opposite angles are in the same straight line

Answer 1

hope it's help you......

Answer 2

To prove= ∠1 + ∠2  + ∠3 = 180°

PROOF:

∠AOC = ∠DOB (Vertically Opposite Angles)

∠1 + ∠6 = ∠3 + ∠4

2∠1 = 2∠3

∠2 = ∠5 (V.O.A)

∠1 + ∠2  + ∠3 + ∠4  + ∠5  + ∠6 = 360°

2∠1 + 2∠2 + 2∠3 = 360°

2(∠1 + ∠2  + ∠3) = 360°

∠1 + ∠2  + ∠3 = 180°

∴Proved