Question

AOB is a straight line. OP bisects angle BOC and OQ bisect angle AOC show that angle POQ is a right angle.​

Answer 1

Answer:

∠POQ= ∠POC+COQ

1/2 ∠BOC+1/2 ∠AOC

∵OP Bisects ∠AOC

∵ ∠POC=1/2 ∠BOC

∵OQ bisects ∠AOC

∵ ∠COQ=1/2 AOC

1/2 (∠BOC+ ∠AOC)

1/2 180 ° (linear pair)

=90 °

Hence proved