Question

OP is angle bisector of an angle AOB of 120 degree. OQ and OR are angle bisectors of angles AOP and BOP respectively. Find the measure of angle QOR.

Answer 1

Answer:

Here OP bisect ∠BOC

∴∠POC=∠BOP …………(i)

and OQ bisect ∠AOC

∴∠AOQ=∠COQ …………….(ii)

and ∠AOB=180

o

[∵AOB is a straight line]

⇒∠BOP+∠DOC+∠COQ+∠AOQ=180

o

⇒∠POC+∠POC+∠COQ+∠COQ=180

o

[using (i) & (ii)]

⇒2∠POC+2∠COQ=480

o

⇒2(∠POC+∠COQ)=180

o

⇒2∠POQ=180

o

⇒∠POQ=90

o

.

Step-by-step explanation: