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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.
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Solution
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^@`
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