In triangle abc, d is a point on side ac such that bd=dc and angle bcd measures 70 degrees. what is the measure if of angle adb?

If BD=DC that means triangle CDB is isosceles triangle and the measure of angles ∡CDB and ∡BCD is the same
                                                 ∡CDB=∡BCD=70°

The angles ∡ADB and ∡CDB are adjacent and suplementary angles

It means  ∡ADB + ∡CDB = 180°
                ∡ADB = 180° - ∡CDB
                ∡ADB = 180° - 70°
                ∡ADB = 110°