If 2 parallel lines are cut by a transversal then the bisectors of interior angles on the same side of transversal intersects each other at
A)60 degree
B)90 degree
C)100 degree
D)120 degree
Define your answer
90 degree .
OB bisects the ∠EBA and OA bisects the ∠BAD.
consider △AOB,∠BAO=2θ
∠OBA=21(180−θ)=90−2θ
∠BAO+∠OBA+∠BOA=180°
⟹90−2θ+2θ+∠AOB=180°
⟹∠AOB=90°
∴ the bisectors of internal angles on the same side of the transversal intersects at right angles.
Let the angle at which the transversal intersects the lines be θ
So, ∠BAD=θ,∠EBA=180−θOB bisects the ∠EBA and OA bisects the ∠BAD.
consider △AOB,∠BAO=2θ
∠OBA=21(180−θ)=90−2θ
∠BAO+∠OBA+∠BOA=180°
⟹90−2θ+2θ+∠AOB=180°
⟹∠AOB=90°
∴ the bisectors of internal angles on the same side of the transversal intersects at right angles.