In a circle centered at point O, diameters AD and BC are drawn, and the angle OAB is 70 °. Find the angle of OCD

Consider the triangle AOW. This triangle is isosceles, because OA and OB are the radii, therefore they are equal.
By the property of an isosceles triangle, ∠OAB = ∠OBA.
Consider the triangles AOW and COD. ∠DOC = ∠AOB, because they are vertical. СО = DO = OB = OA, because these are the radii of a circle.
Consequently, the triangles AOW and COD are equal (by the first sign). Therefore, ∠OBA = ∠OAB = ∠ODC = ∠OCD = 70 °
Answer: ∠OCD = 70