In a circle with center O, segments AC and BD diameters. The central angle AOD is equal to 122. Find the angle ACB
| August 13, 2021 | education
Before solving the task, you need to make a drawing.
Angle AOD and angle AOB are adjacent. AOD + AOB = 180 °.
Angle AOB = 180 ° – 122 ° = 58 °.
Angle AOB – central, rests on the arc AB.
The sought angle ACB – the inscribed angle, also rests on the arc AB.
The inscribed angle is equal to half of the central angle resting on the same arc. This means that the angle ACB is equal to half the angle AOB.
ACB angle = 1/2 * 58 ° = 29 °.
Answer: Angle ACB = 29 °.
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