Question

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

Answer 1

consider a triangle ABC. then suppose the bisectors of <B and <C intersects each other at point D .then we know that that angle(<)A=2<BDC- 180.and it is given that the angle between the two bisectors of <B and <C is 135°.so <BAC=270°-180°=90°.thus the triangle is a right triangle.