Quadrilateral ABCD is inscribed in a circle, ABD angle is 82 degrees, CAD angle is 28 degrees. Find the angle ABC.
| February 11, 2021 | education
The inscribed angle of AВD = 820 and rests on the arc of AD, then the degree measure of the arc of AD = 2 * 82 = 164.
The inscribed angle СAD = 280 and rests on the arc of the СD, then the degree measure of the arc of the СD = 2 * 28 = 56.
Then the degree measure of the arc ADС = ᵕAD + ᵕСD = 164 + 56 = 220.
The inscribed angle ABC rests on the ADС arc and is equal to half of its degree measure. Angle ABC = 220/2 = 110.
Answer: The angle ABC is 110.
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