8. ABC is a triangle in which ZA = 72°, the internal bisectors of angles B and c meet in o. find the magnitude ofएंगल एबीसी
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Angle at O = 126°
Step-by-step explanation:
In ΔABC, ∠A + ∠B + ∠C = 180°
∠B + ∠C = 180° - ∠A = 180° - 72° = 108° . . . . . . . . (i)
As the internal bisectors of angle B and C meet at O,
In ΔBOC, Angle at O + ∠B/2 + ∠C/2 = 180°
=> Angle at O = 180° - (∠B/2 + ∠C/2) = 180° - 1/2(∠B + ∠C) = 180° - 54° = 126°
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