In an isosceles triangle ABC,the bisector of angle B and angle C meet at O.If angle BOC= 140 degree,then angle A measures ?

Answer :

We form our diagram from given information , As :

Here , BOC  =  140°

And

AB  =  AC ( triangle ABC is a isosceles triangle )  From base angle theorem we get

ABC  =  ACB  =  x  , So

OBC  =  OCB  =  ABC2 =  ACB2 = x2

Now from angle sum property in triangle BOC we get

OBC  +  OCB  +  BOC  =  180° , Substitute values and get

x2 + x2 + 140° =  180°2x2   =  40°x =  40°
So,
ABC  =  ACB  = 40°

Now we get from angle property in triangle ABC

ABC  +  ACB  +  BAC  = 180°

40°  + 40°  + BAC  = 180°

BAC  = 100°                                                                                      ( Ans )

  • 1
What are you looking for?