Since "ABC is an isosceles triangle with BA=BC"
Therefore, angle BAD= angle BCA (Let it be y) (1)
"D lies on AC, ABD is an isosceles triangle with AB=AD"
AB=AD means that angle ABD= angle ADB = 72 degrees. (since ABD=72 (given))
so we can find y now.
in a triangle, the sum of angles is equal to 180 degrees.
Then, 180=72+72+y, y=180-144=36
we have found y and from (1) we conclude that also angle BCA= 36 degrees.
Since angle on straight line = 180
Straight-line ADC have angle BDA=72, so the other angle BDC=180-72=108
In triangle BCD, since it is a triangle, angles add up to 180
then angle CBD= 180-108-36=36 as well.
So angle DBC= angle DCB