Bisectors of angle B and angle C of a triangle ABC intersect each other at point O.Prove that angle BOC=90 degree+half of angle A.

In a triangle ABC, we have :

angle[A+B+C] = 180 DEGREE [since,sum of the angles of a tri.]

=> 1/2[A+B+C] = 90 DEGREE

=> 1/2A + angle1+angle2 = 90 degree

=> angle1 + angle2 = 90 - 1/2angle A -------------- equation 1

NOW in trianglel OBC,

angle1 + angle2 + angle BOC = 180

90 - 1/2 angleA + angle BOC = 180 FROM 1

angle BOC = 90degree + 1/2 angle A.

Hence,it is proved.