Question

in figure OP bisects angle BOC and OQ bisects AOC show that Angle POQ = 90°

Answer 1

 OP bisects ∠BOC 

∴ ∠POC = 1/2 ∠BOC ...(i) 

 Also OQ bisects ∠AOC 

∴ ∠COQ = 1/2 ∠AOC ...(ii) 

∴ OC stands on AB 

∴ ∠AOC + ∠BOC = 180 [Linear pair] 

⇒ 1/2 ∠AOC + 1/2 ∠BOC = 1/2 × 180

⇒ ∠COQ + ∠POC = 90 [Using (i) & (ii)] 

⇒ ∠POQ = 90 [By angle sum property] 

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Answer 2

Answer:

AOB= 90°

BOC= 90°

According to the question.

OP bisects angle BOC and PQ bisects angle AOC.

Since.

QOC=45°

POC=45°

then POQ= 90°