# AC and BD are diameters of a circle with center O. The angle of ACB is 74 °. Find the angle of the AOD.

May 31, 2020 | Education

| Consider the triangle OCB.

OB = OC (because these are the radii)

Therefore, the triangle OCB is isosceles.

Then ∠ACB = ∠CBD = 74 ° (by the property of an isosceles triangle).

By the theorem on the sum of the angles of a triangle:

180 ° = ∠ACB + ∠CBD + ∠BOC

180 ° = 74 ° + 74 ° + ∠BOC

∠BOC = 32 °

∠BOC = ∠AOD = 32 ° (as they are vertical).

Answer: 32

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.