Question

In an isosceles triangle ABC,AC=BC,angle BAC is bisected by AD whereD lies on BC.It is found that AD=AB.Then angle ACB equals

Answer 1

Given AC = BC. Then angles B and A are equal. Let them be equal to 2x.

AD bisects angle A. Then angle BAD = x

Given that AD = AB, in triangle BAD,,angles ADB and DBA are equal.

Angle DBA is angle B = 2x. Then, in triangle BAD, the sum of all the three angles (BAD + ADB + DBA = x + 2x + 2x) = 5x = 180 Or x=36 degree

In the triangle,angles B and A equal 2x = 72 degree

Thus, angle ACB = 36 degrees

Hope this helps.