Question

If the bisectors of angle ABC and angle Acb of a triangle ABC meet at O prove that angle BOC= 90 degree + 1/2 angle A

Answer 1

First draw the rough figure of the triangle and then relate the following answer

In triangle ABC :

angle ABO=angleOBC=x becoz BO is bisector

angle ACO=angleOCB=y becoz oc is bisector

therefore in triangleABC :

x+x+y+y+angleA =180 ....... angle sum prop. of triangle

2x+2y+angleA=180

2(x+y) +angle A =180

x+y = 90 - 1/2*angleA ..............by shifting the values

in Triangle OBC :

x+y+angleBOC=90 degree.

90-1/2*angleA +angleBOC =180 by substituting value of x+y

angle BOC=180-90+1/2angleA

angle BOC= 90+1/2angle A

hence it is prooved....

hope it helped you