Question

In a triangle ABC, angle A is the vertex angle=70, angle ABC =54. If BO and OC are the bisectors of angle ABC and ACB respectively of Triangle ABC, find angle BOC.

Answer 1

Answer:

angle BOC = 125°

Step-by-step explanation:

In triangle ABC we have

angle A + angle ABC + angle ACB = 180° ( since sum of all angles is 180°)

70° + 54°+ angle ACB = 180°

angle ACB = 56°

now angle ABC = angle ABO + angle OBC

angle ABO = angle OBC = 54/2=27°

now angle ACB = angle ACO + angle OCB

angle ACO = angle OCB = 56/2 = 28°

in triangle BOC

angle OBC + angle OCB + angle BOC = 180°

27° + 28° + angle BOC = 180°

angle BOC = 125°