Question

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

Answer 1

Given the bisectors the base angles of an triangle enclose an angle of `135^@` 

i.e., ∠BOC=`135^@` 

But, W.K.T 

 

`∠ BOC=90^@+1/2∠B` 

⇒ `135^@=90^@+1/2∠A` 

⇒`1/2∠A=135^@-90^@` 

⇒`∠A=45^@(2)` 

⇒`∠A=90^@`

∴ ΔABC is right angled triangle right angled at A.