In △abc, d is a point on side ac such that bd=dc and ∠bcd measures 70∘. what is the degree measure of ∠adb?

BD=DC => △BCD is an isosceles triangle => ∠BCD=∠DBC=70°.
Sum of the degrees measures in a triangle = 180° =>
180=∠BCD+∠DBC+∠CDB;
180=70+70+∠BCD
∠BCD=40°

∠ADB and ∠BCD are adjacent => 
∠ADB+∠BCD=180
∠ADB+40=180
∠ADB=140°