Answer:
Triangle ABD is isosceles with AB = AD
=> angle ADB = angle ABD = 72 deg
The sum of 3 angles inside triangle ABD is equal to 180 deg
=> angle BAD + angle ADB + angle ABD = 180 deg
=> angle BAD = 180 - angle ADB - angle ABD = 180 - 72 -72 = 36 deg
Triangle ABC is isosceles with BA = BC
=> angle BCA = angle BAC = angle BAD = 36 deg
=> angle BCD = angle BCD = 36 deg (1)
The sum of 3 angles inside triangle ABC is equal to 180 deg
=> angle ABC + angle BCA + angle BAC = 180 deg
=> angle ABC = 180 - angle BCA - angle BAC = 180 - 36 - 36 = 108 deg
As shown in picture,
angle ABD + angle CBD = angle ABC
=> angle CBD = angle ABC - angle ABD = 108 - 72 = 36 deg (2)
From (1) and (2)
=> angle CBD = angle BCD = 36 deg
=> triangle CDB is isosceles with DC = DB
Hope this helps!
:)
