If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.

Question

If the bisectors of the base angles of a triangle enclose an angle of 135&#xB0;, prove that the triangle is a right triangle.

Philoid · Accepted Answer

Given bisector og the base angles of a triangle enclose an angle of 135^o

i.e. ∠BOC = 135^o

But,

135^o = 90^o + ∠A

∠A = 135^o – 90^o

∠A = 45^o (2)

= 90^o

Therefore, is right angled triangle right angled at A.