Question

ABC is a triangle in which ∠A — 72°, the internal bisectors of angles B and C meet in O.
Find the magnitude of ∠BOC.

Answer 1

 

Given, 

ABC is a triangle 

`∠ A=72^@` and internal bisector of angles B and C meeting O 

In` Δ ABC = ∠ A+∠ B+∠ C=180^@` 

⇒`72^@+∠ B+∠ C=180^@` 

⇒`∠ B+∠C =180^@-72^@ ` divide both sides by ‘2’ 

⇒`∠ B/2+∠ C/2=108^@/2`              ..................(1) 

⇒`∠ OBC +∠ OCB =54^@`             ...................(1) 

Now in `Δ BOC⇒ ∠OBC +∠ OCB +∠ BOC    = 180^@` 

⇒ `54^@+∠BOC=180^@` 

⇒ `∠BOC=180^@-54^@=126^@` 

∴`  ∠ BOC=126^@`