Question

15. If two straight lines intersect each other then prove that the ray oppo
to the bisector of one of the angles so formed bisects the vertica
opposite angle.
16. Prove that the bisectors of two adjacent supplementary angles i
a right angle.
sind.​

Answer 1

Given AB and CD are straight lines which intersect at O. OP is the bisector of ∠ AOC.

To prove : OQ is the bisector of ∠ BOD

Proof :

AB, CD and PQ are straight lines which intersect in O.

∠ AOP = ∠ BOQ (vertically opposite angles)

∠ COP = ∠ DOQ (vertically opposite angles)

∠ AOP = ∠ COP (OP is the bisector of ∠ AOC)

∴ ∠ BO

Thus, the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

Similarly, the bisector of ∠ AOD also bisects the ∠ BOC.