Question

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ABC is a triangle in which ∠A = 72⁰, the internal bisector of angles B and C meet in O. Find the magnitude of ∠BOC.​

Answer 1

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We know that the sum of all angles of a triangle is 180°

in which angle A=72°

That means,

A+B+C=180°

72o+B+C=180°

B+C=180°− 720 = 108…(i)

and we are also given that internal bisector of Angle B and Angle C meet at O

Hence, dividing equation (i) with 2 on both sides we get,

12(B+C) = 1082 = 54°

12(B+C) mean angle angle OBC+ angle OCB = 54°

also, OBC is a triangle where, all angle sum 180°

⟹ Angle BOC=180°−54° = 126°

Answer 2

Answer:

The value of angle BOC=126°