Question

1. 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

Answer:

HOPE IT HELPS

Step-by-step explanation:

If. AOC IS 50 DEGREE THEN AOC+COB=180 (LINEAR PAIR)

BOC=180-50=130

POQ= HALF OF AOC+HALF OF BOC=30+65=95

Answer 2

Answer:

i) ∠BOC

∵ AOB is a straight line (straight angle.)

∴ m∠BOC = 180 - m∠AOC

m∠BOC = 180 - 60

m∠BOC = 120°

ii) ∠POQ

∵ line OP bisects BOC,   line OQ bisects AOC

∴ m∠BOP & m∠POC =  m∠BOC/2

m∠BOP & m∠POC = 120/2

m∠BOP & m∠POC = 60°   (1)

∴  m∠AOQ & m∠QOC =  m∠AOC/2

m∠AOQ & m∠QOC =  60/2

m∠AOQ & m∠QOC =  30°  (2)

From (1) and (2)

m∠POQ = m∠POC + m∠QOC

m∠POQ = 60 + 30

m∠POQ = 90°