ABC is a triangle in which ∠A=72∘, the internal bisectors of angles B and C meet in O. Find the magnitude of ∠BOC.
In ΔABC,∠A=72∘ and bisectors of ∠B and ∠ C meet at O.
Now ∠B+∠C=180∘−72∘=108∘
∵ OB and OC are the bisectors of ∠B and ∠Crespectively
∴ ∠OBC+∠OCB=12(∠B+∠C)
=12×108∘=54∘
But in ΔOBC,
∴∠OBC+∠OCB+∠BOC=180∘
⇒54∘+∠BOC=180∘
∴∠BOC=180∘−54∘=126∘