These lines are perpendicular
because if you graph them they intersect and form right angles.
another way you know that they are perpendicular is reciprocal slopes
meaning they are totally opposite or (flipped)
Alright, lets get started.
Please refer the diagram, I have attached.
∠ABC is given as y.
So, the ∠EBC will be 180 - ∠ABC.
∠EBC = 180 - y
As given in question, BO is the bisector of ∠EBC, it means ∠OBC will be half of the ∠EBC.
∠OBC = of ∠EBC
∠OBC = (180 - y)
∠OBC =
Similarly,
the ∠DCB will be 180 - ∠ACB
∠DCB = 180 - z
As given in question, CO is the bisector of ∠DCB, it means ∠OCB will be half of the ∠DCB.
∠OCB = of ∠DCB
∠OCB = (180 - z)
∠OCB =
In triangle OBC, the sum of the angles of the triangle will be 180.
∠BOC + + = 180
∠BOC +
∠BOC = =
As per upper triangle ABC,
or
Putting this value in value of ∠BOC
∠BOC =
∠BOC =
∠BOC = 90 - : Hence proved
Hope it will help :)