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Question
In Δ ABC, if u∠B = 60°, ∠C = 80° and the bisectors of angles ∠ABC and ∠ACB meet at a point O, then find the measure of ∠BOC.
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Solution
In ΔABC, ∠B = 60, ∠C = 80 and the bisectors of ∠B and ∠C meet at O.
We need to find the measure of ∠BOC
Since,BO is the bisector of ∠B
∠OBC = 1/2 ∠B
`= 1/2 (60°)`
= 30°
Similarly,CO is the bisector of ∠C
`∠OCB 1/2 ∠C`
= 1/2(80°)
= 40°
Now, applying angle sum property of the triangle, in ΔBOC, we get,
∠OCB + ∠OBC + ∠BOC = 180°
30° + 40° + ∠BOC = 180°
∠BOC + 70° = 180°
∠BOC = 180°- 70°
= 110°
Therefore, ∠BOC = 110°.
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