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 α.

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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   α.

Aubrie Conley · Accepted Answer

In the triangle ABC, the interior angles are:   ∠  A  =  a  ,  ∠  B  =  x  ,  ∠  C  =  180  −  a  −  x.External corners: in   ∠  B  =  180  −  x and in   ∠  C  =  a  +  x.In a triangle BOC, by condition, the angles are equal:  ∠  O  B  C  =  i  n  ∠  B      /    2  =  (  180  −  x  )      /    2  =  90  −  x      /    2  ;  ∠  O  C  B  =  i  n  ∠  C      /    2  =  (  a  +  x  )      /    2  =  a      /    2  +  x      /    2.Then   ∠  B  O  C  =  180  −  ∠  B  O  C  −  ∠  O  C  B  =  180  −  (  90  −  x      /    2  )  −  (  a      /    2  +  x      /    2  )  =  90  −  a      /    2

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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