Triangle ABC is isosceles with AB=BC. There is a point D on AC such that BD = DC and AB=AD.

What is the measure of angle BAC?

 

 

                
                  B

     A                 D        C

Triangles BAD and BDC are both isosceles. Thus angle BAD = angle BCD = a, say, and angle ABD = angle BDA = b, say and

1) a+2b=180 and

2) 2a+180-b=180.

From 2) we get b=2a and putting this in 1) gives 5a=180 so that a=36.

Edited on September 1, 2004, 2:17 pm

Posted by Richard on 2004-09-01 14:14:34