In triangle ABC, angle A = 56 degrees.  The bisectors of angle B and angle C meet at point O.  Find angle BOC.

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Answer : 

Given  ​In triangle ABC and bisectors of angle B and angle C meet at ' O ' 
And
$\angle$ A  = 56$°$



In Triangle ABC , we know from angle sum property 

$\angle$ A + $\angle$ B  +  $\angle$ C   =  180$°$

56$°$ +  $\angle$ B  +  $\angle$ C   =  180$°$

 $\angle$ B  +  $\angle$ C   =  124$°$                                                      ------------------ ( 1 ) 

Now
In Triangle OBC , we know from angle sum property 

$\angle$ OBC + $\angle$ OCB  +  $\angle$ BOC   =  180$°$

$\frac{1}{2}\angle$ B + $\frac{1}{2}\angle$ C  +  $\angle$ BOC   =  180$°$                              ( As given angle bisector of $\angle$ B  and $\angle$ C m eet at O )

Taking LCM we get 

 $\angle$ B  +  $\angle$ C   +  2 $\angle$ BOC     =  360$°$

124$°$ +  2 $\angle$ BOC     =  360$°$                                  (  From  equation 1  )

 2 $\angle$ BOC    =  236$°$  

$\angle$ BOC    =  118$°$                                                ( Ans )

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