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

Let ABC be a triangle and Let BO and CO be the bisectors of the base anglerespectively.

We know that if the bisectors of angles ∠ABC and ∠ACB of a triangle ABC meet at a point O, then

$\angle BOC=90°+\frac{1}{2}\angle A$

$$\begin{gathered} \therefore 135°=90°+\frac{1}{2}\angle A \\ \Rightarrow 45°=\frac{1}{2}\angle A \\ \Rightarrow \angle A=90° \end{gathered}$$

Hence the triangle is a right angled triangle.