# The lines containing the bisectors of the exterior angles at vertices B and C of triangle ABC intersect at point O. find angle BOC if angle A is equal to alpha

The lines containing the bisectors of the exterior angles at vertices B and C of triangle ABC intersect at point O. find angle BOC if angle A is equal to $\alpha$.
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Aubrie Conley
In the triangle ABC, the interior angles are: $\mathrm{\angle }A=a,\mathrm{\angle }B=x,\mathrm{\angle }C=180-a-x$.
External corners: in $\mathrm{\angle }B=180-x$ and in $\mathrm{\angle }C=a+x$.
In a triangle BOC, by condition, the angles are equal:
$\mathrm{\angle }OBC=in\mathrm{\angle }B/2=\left(180-x\right)/2=90-x/2;$
$\mathrm{\angle }OCB=in\mathrm{\angle }C/2=\left(a+x\right)/2=a/2+x/2.$
Then $\mathrm{\angle }BOC=180-\mathrm{\angle }BOC-\mathrm{\angle }OCB=180-\left(90-x/2\right)-\left(a/2+x/2\right)=90-a/2$