Q. 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°?

Question

anonymous · Answer

r u not having a sketch with u?

phi · Answer

http://openstudy.com/groups/mathematics/updates/4e6385280b8b1f45b4ac268d

anonymous · Answer

phi its nice
but i want in the way of class 9
the things in ur answer are not even taught to us :P

phi · Answer

Here's another way, that uses geometry theorems.  Have you heard of these?


Thm
 2 triangles are similar if an angle of one triangle is congruent to an angle of the other triangle, and if the the measures of the sides that include the angle are proportional

Thm 
The bisector of angle of a triangle divides the opposite side into segments whose measures are proportional to the measures of the other two sides of the triangle.

phi · Answer

Here's a way. See attached.