Question

Equilateral triangle ABC and isosceles triangle DBC share side BC. If angle BDC=34 and BD=BC, what is the measure of angle ABD

Answer 1

f BC=BD, then 
∠BDC=∠BCD=34° (angles opposite equal sides) 

Hence ∠CBD=180-(34+34)=112° 
∠ABD=∠ABC+∠CBD=? 

Recall that ΔABC is equilateral.

Answer 2

The measure of angle ABD would be 73 degrees.