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Vertically Opposite Angles

In the triang...

Question

In the triangle ABC, the bisectors of the exterior angles B and C meet at O. Given angle $B A C = 60^{\circ}$ and angle $A B C = 70^{\circ}$ . Find angle BOC.

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Solution

$∠ A C B = 180^{\circ} - (∠ B + ∠ A)$
$= 180^{\circ} - (70 + 60)$
$= 50^{\circ}$
$∴ ∠ B O C = 180^{\circ} - (∠ O B C + ∠ O C B)$
$= 180^{\circ} - (35^{\circ} + 25^{\circ})$
$= 120^{\circ}$

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