Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ABC is equal to BOC
Given, ABC is an isosceles triangle
AB = AC (Given))
To prove : External angle adjacent to ABC is equal to BOC
Proof : Produce line CB to D in ABC
AB = AC (Given)
ACB = ABC (angles opposite to equal sides are equal)
OCB = OBC (Bisector of angle B and C, respectively)
In BOC,
OBC + OCB + BOC = 180°
2OBC + BOC = 180° (From above)
ABC + BOC = 180°
( ABO + OBC = ABC)
ABC+ OBA = 180°
OBA = BOC.
Hence proved.