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Question
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
Options
60°
120°
150°
30°
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Solution
In the given ΔABC,∠A = 60° and ∠B = 80° . Bisectors of ∠B and ∠C meet at O.
We need to find ∠BOC
Since, OB is the bisector of ∠B.
Thus, `∠OBC = 1/2 ∠ABC ..... (1)`
Now, using the angle sum property of the triangle
In ΔABC, we get,
∠A + ∠B + ∠C =180°
60° + 80° + ∠C = 180°
140° + ∠C = 180°
∠C = 180° - 140°
∠C = 40°
Similarly, in ΔBOC
∠OBC + ∠O + ∠OCB = 180
∠O + 20° + 40°=180°
∠O + 60° = 180°
∠O = 180° - 60°
= 120°
Hence, ∠BOC = 120°
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