Question

ABC is a triangle in which angle A is equal to 72 degree the internal bisectors of Angle B and C meet in a find the magnitude of angle BOC​

Answer 1

Answer:

1) < BAC = 72. ... ( Given )

2 ) < BAC + < ABC + < ACB = 180. ... ( angle sum property of triangles

3 )》72 + < ABC + < ACB = 180

》< ABC + < ACB = 180 - 72

》< ABC + < ACB = 108

4 )Dividing both the sides by 1/2 we get ,

》< ABC/2 + < ACB/2 = 108/2

But < ABC/2 = < OBC & < ACB/2 = < OCB

5) Hence

< OBC + < OCB = 54

6)If we consider Triangle BOC

< OBC + < OCB + < BOC = 180. ... ( Angle sum property of triangles )

7) But < OBC + < OCB = 54. .. ( from 5 )

》54 + < BOC = 180

》< BOC = 180 - 54

》< BOC = 126

Hope it helps you ..!!