in the figure B and so are the bisector of Angle B and C respectively if angle BAC is equal to 80 degree and Angle ACB is equal to 30 degree find angle BOC and angle OBC
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What is the angle BOC if in ∆ABC, the angle bisectors of angle B and C meet at O, and if angle A = 60°?
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Ved Prakash Sharma
Answered November 30, 2018
ABC is a triangle in which A=60°, bisectors of angles B and C meet at point O.
In triangle ABC
60°+B+C=180°. or. B+C=120°…………….(1)
B0 is bisector of. angle B and CO is bisector of angle C . Thus
angle OBC=B/2. , angle. OCB = C/2.
In triangle OBC
angle BOC+ angle OBC. + angle OCB. =180°
angle BOC. +B/2 +C/2=180°
angle BOC = 180°- 1/2(B+C). Putting B+C=120° from eqn.(1)
angle BOC. = 180°-1/2(120°) = 180°-60°. = 120°. Answer.
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