If the bisector of the base angles of a triangle enclosed an angle of 135o, prove that the triangle is a right triangle.
In △ABC,BO and CO are bisectors of angle B and C respectively.
Now, in △ABC,
∠A+∠B+∠C=180°
∠B+∠C=180°−∠A.....(1)
Now, in △BOC,
∠BOC+12∠B+12∠C=180°
12(∠B+∠C)=180°−135°(∵∠BOC=135°)
12(180°−∠A)=45°
⇒180°−∠A=90°
⇒∠A=90°
⇒△ABC is a right triangle.
Hence proved.