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

bystudin | 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

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