Question
In a ΔABC, the internal bisectors of ∠B and ∠C meet
at point O. Find the measure of ∠BOC if the measure of ∠BAC = 50 ° .Solution
Let ∠ABC = 2x o and ∠ACB = 2y o
Sum of all the angles of a triangle is 180 o
So, ∠BAC + ∠BCA + ∠CBA = 180 o
50 o + 2x + 2y = 180 °
2x + 2y = 130 °
x + y = 65 °
Again, in ΔBOC, ∠BOC + ∠BCO + ∠CBO = 180 o
So, ∠BOC + x + y = 180 °
So, ∠BOC = 180 ° – 65 ° = 115 °
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