In a circle centered at point O, diameters AD and BC are drawn, and the angle ABO is 80 °. Find the ODC angle

Consider the triangle AOB. This triangle is isosceles, because OA and OB are the radii, so they are equal.
By the property of an isosceles triangle, ∠OAB = ∠ABO = 80 °.
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 = 80 °
Answer: ∠ODC = 80 °

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.