Question

if one of the angles of a traingle is 130° then the angle between the bisectors of the other two angles can be
(a)50°
(b)65°
(c)145°
(d)155°​

Answer 1

Answer:

consider a∆ABC, such that angle BAC = 130°

and bisectors of angle B and angle C meet an O

to find: angle BOC

now, in ∆ABC ,

angle BAC +angle ABC+ angle ACB= 180°

130+ABC+ACB= 180 (angle sum properly)

angle ABC +angle ACB = 50

1/2(angle ACB +angle ACB)= 25

angle OBC+angle OCB =25 ( OB and OC bisect angle ABC and angle ACB )

now, in ∆ OBC,

angle OBC + angle OCB+ angle BOC = 180

25+ angle BOC = 180

angle BOC = 155