Question

ABC is a triangle in which angle B= 2 angle C. D is a point on BC such that AD bisects angle BAC and AB=CD. Prove that angle BAC=72°

Answer 1

so Triangle ABC and ADC are similar (two sides and one angle is equal)so angle CAD = angle ACB =cso angle BAC=2cand in triangle ABCangle BAC + angle ABC + angle ACB = 2c+2c+c = 5c = 180c=180/5 = 36angle BAC =2c=2*36 =72