Find the degree measure ABC if CD is the diameter of the circle and the angle ABD is 110 degrees rad.
| January 17, 2021 | education
The inscribed angle of the AED, according to the condition, is 110, then the degree measure of the arc of the AED on which this inscribed angle is based is equal to two degree measures of the inscribed angle.
Arc AСD = 2 * 110 = 220.
СD – the diameter of the circle, then the degree measure of the arc СD = 180.
The degree measure of the AC arc is equal to the difference between the degree measures of the arcs of the ACD and the СD.
Arc AC = AСD – SD = 220 – 180 = 40.
The sought, inscribed angle ABC rests on the arc AC, then the angle ABC = 40/2 = 20.
Answer: The angle ABC is 20.
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