The AC and BD are the diameters of the circle centered on O. The angle acb is 74. Find the angle AOD. Give your answer in degrees.

To solve this problem, you need to imagine what the inscribed and central angles are. The inscribed angle is half the central angle resting on the same arc. Conversely, the central angle is twice the inscribed angle resting on the same arc.

Draw a circle with center O, two diameters AC and ID (that is, they must intersect at point O).

1. Angle ACB = 74 degrees (by condition), find its central angle. This angle rests on the arc AB, so the central angle will be AOB. Angle AOB is twice the angle AOB, AOB = 74 * 2 = 148 degrees.

2. Angle AOB and angle AOD are adjacent, their sum is 180 degrees.

AOB + AOD = 180

148 + AOD = 180

AOD = 180 – 148 = 32

Answer: The angle of the AOD is 32 degrees.