Question

prove that the bisected of a pair of vertically opposite angles are in the same straight line. ​

Answer 1

Answer:AB and CD are straight lines intersecting at O. OX the bisector of angles ∠AOC and OY is the OY is the bisector of ∠BOD. OY is the bisector of ∠BOD.∴ ∠1 = ∠6  … (1)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°.∴ ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 360°⇒ ∠1 + ∠2 + ∠3 + ∠3 + ∠2 + ∠1 = 360°  (Using (1), (2) and (3))⇒ 2∠1 + 2∠2 + 2∠3 = 360°⇒ 2(∠1 + ∠2 + ∠3) = 360°⇒ ∠DOY + ∠AOD + ∠AOX = 180°⇒ ∠XOY = 180°∴ The bisectors of pair of vertically opposite angles are on the same straight line.

Step-by-step explanation: