Question

13. If one of the angles of a triangle is 130°, then the angle between the bisectors of
other two angles will be​

Answer 1

Consider a △ABC,such that ∠BAC=130∘ and bisectors of ∠B and ∠C meet at O.

To find: ∠BOC

Now, in △ABC,

∠BAC+∠ABC+∠ACB=180

130+∠ABC+∠ACB=180 (Angle sum property)

∠ABC+∠ACB=50

21(∠ABC+∠ACB)=25

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

Now, in △OBC,

∠OBC+∠OCB+∠BOC=180

25+∠BOC=180

∠BOC=155∘.

Answer 2

Answer:

50° and 25° each..........