The quadrilateral ABCD is inscribed in a circle. The ABC angle is 128 °, the CAD angle is 73 °. Find the angle ABD.
| February 19, 2021 | education
The inscribed angle СAD = 73 and rests on the arc of the СD, then the degree measure of the arc СD = 2 * 73 = 146.
The inscribed angle ABC = 1280 and rests on the ADС arc, then the degree measure of the ADС arc = 2 * 128 = 256.
Then the degree measure of the arc AD = ᵕADС – ᵕСD = 256 – 146 = 110.
The inscribed angle of the AВD rests on the AD arc and is equal to half of its degree measure. Angle AВD = 110/2 = 55.
Answer: The value of the AВD angle is 55.
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