Answer: (A) 35 degrees
Step-by-step explanation:
(I am assuming the 70 degrees measure refers to the central angle <ACB)
The "easy" way: clearly the angle <ADB must but smaller than <ACB (this follows from a simple triangle argument) and given that the only choice of an angle smaller than 70 degrees is (A) 35 degrees, that should be the correct pick without showing work. But we can do better.
The principled way: let us actually determine the measure <ADB. Connect the points DC with a line segment starting at D, crossing C, bisecting <ACB and ending intersecting the arc at a point, say, E. The angle <ECB=35 degrees, therefore the angle <BCD=180-35=145 degrees. Therefore <BDC=17.5 degrees. Since the triangle ABD is isosceles, <CDB = <CDA. Therefore <ADB = 2*17.5=35 degrees.