Question

In Fig. 4.50, BO and CO are the bisectors of exterior angles angle B and angle C of ∆ABC. Find angle BOC.​

Answer 1

Answer:

70° is the Answer of your

Answer 2

Answer:

Given: BO is the bisector of ∠CBE

         OC is the bisector of ∠BCF

To Find : ∠BOC

SOLUTION:

if ∠ABC=50°, then

∠ABC+∠OBC+∠OBE=180°                                          (∴∠OBC=∠OBE=x)

∠ABC+x+x=180°

∠ABC+2x=180°

50°+2x=180°

2x=180°-50°

2x=130°

x=65°

and

if ∠BCA=60°,then

∠BCA+∠BCO+∠OCF=180°                                (∴∠BCO=∠OCF=y)

∠BCA+y+y=180°

∠BCA+2y=180°

60°+2y=180°

2y=180°-60°

2y=120°

y=60°

In ΔBOC,

x+y+∠BOC=180°                                      ( Angle Sum Property)

65°+60°+∠BOC=180°

125°+∠BOC=180°

∠BOC=55°

HENCE PROVED

Step-by-step explanation: