Lines AC and BD diameters of a circle with center O angle ACB equal to 74 degrees find the angle AOD.

Triangles AOD and COB are equal, since the angles AOD and COB are vertical, and therefore equal, and OD = OA = OC = OB = r is the radius.

Therefore, from an isosceles triangle of the OWL, the angle of the OWL = 180º – 2 * ACB = 180º – 2 * 74º = 180º – 148º = 32º.

Then, the angle AOD = COB = 32º.

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