Q. 15

In the figure, if AO

Answer :

Ray OP bisects ∠ BOC 
... ∠ COP  = ∠ POB 
... ∠ COP  =  1/2 ∠ BOC           ------------(1)
Ray OQ bisects ∠ AOC
... ∠ AOQ  = ∠ QOC
      ∠ QOC = 1/2 ∠ AOC             -----------(2)
Adding (1) and (2) 
... ∠COP + ∠ QOC = 1/2 [ ∠BOC + ∠ AOC ]    (∠AOC and ∠ BOC form a linear pair.)
                        = 1/2 x 180°                      (Linear Pair Axiom)
                ∠QOP =  90°
            ... ∠POQ is a right angle.

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