Quadrilateral ABCD is inscribed in a circle angle ABD = 85 angle CAD = 19, find ABC.
| April 25, 2021 | education
The inscribed angle ABD = 82 and rests on the arc AD, then the degree measure of the arc AD = 2 * 85 = 170.
The inscribed angle CAD = 19 and rests on the arc CD, then the degree measure of the arc CD = 2 * 19 = 38.
Then the degree measure of the arc is ADC = ᵕAD + ᵕСD = 170 + 38 = 208.
The inscribed angle ABC rests on the arc ADC and is equal to half of its degree measure. Angle ABC = 208/2 = 104.
Answer: The angle ABC is 104.
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