Question

If the bisectors of the base angles of a triangle enclose an angle of $\text{13}{\text{5}}^{\text{o}}$ prove that the triangle is a right triangle.

Answer 1

R.E.F image

Solution :-

Let the bisectors of the base angles B and C of triangle

$ABC$ meet at $O$

Given angle $BOC={135}^{\circ }$

Now In $△BOC$

$\angle OBC+\angle BOC+\angle OCB=180$

$\frac{1}{2}\angle B+{135}^{\circ }+\frac{1}{2}\angle C={180}^{\circ }$

$\frac{1}{2}[\angle B+\angle C]={45}^{\circ }$

$\angle B+\angle C={90}^{\circ }$

In $△ABC$

$\angle A+\angle B+\angle C={180}^{\circ }$

$\angle A+{90}^{\circ }={180}^{\circ }$

$\angle A={90}^{\circ }$

Therefore triangle $ABC$ is an right triangle.