Question

CHALLENGERS
In the following figure, AOB is a straight angle. OQ
is the bisector of AOC and OP is the bisector of BOC.
If | AOC = 60°, then find i) BOC ii) POQ.​

Answer 1

Given : AOB is a straight  line

OQ  is the bisector of AOC

OP is the bisector of BOC

∠AOC = 60°

To Find : ∠BOC  , ∠POQ

Solution:

AOB is a straight  line

∠AOC and  ∠BOC form a linear pair

=> ∠AOC +  ∠BOC = 180°

=>  60° +  ∠BOC = 180°

=>  ∠BOC = 120°

∠POQ  = ∠POC + ∠QOC

∠POC = (1/2) ∠BOC

=>  ∠POC = (1/2) 120°

=>  ∠POC = 60°

∠QOC = (1/2) ∠AOC

=>  ∠QOC = (1/2) 60°

=>  ∠QOC = 30°

∠POQ  = ∠POC + ∠QOC

=> ∠POQ  = 60° + 30°

=> ∠POQ  = 90°

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