Question

in triangle abc,/a=50° and the external bisectors of/b and/ceet at o .what is the measure of triangle boc​

Answer 1

Answer:

In △ABC,

∠ABC+∠ACB+∠BAC=180

∠ABC+70+50=180

∠ABC=60

∘

∠OCB=

2

1

(180−∠ACB)

∠OCB=

2

1

(180−50)

∠OCB=65

∘

∠OBC=

2

1

(180−∠ABC)

∠OBC=

2

1

(180−60)

∠OBC=60

∘

In △OBC,

∠OCB+∠OBC+∠BOC=180

65+60+∠BOC=180

∠BOC=180−125

∴∠BOC=55

∘