Question

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

Answer 1

In ∆ ABC, let the bisectors of angle B and C meet at O

therefore, angle BOC=135°

In ∆BOC,

➡angle BOC+angle BCO+angle CBO=180°

➡135+1/2(angle B)+1/2(angle C)=180°

➡1/2(angle B+angle C)=45°

➡angle B+angle C=90°-----------1.)

In ∆ ABC

➡angle A + angle B + angle C =180°

➡angle A + 90°=180° [ from-1 ]

➡angle A=90°

Hence ABC is a right angled triangle