Quadrilateral ABCD is inscribed in a circle, angle ABC = 125 degrees, angle CAD = 55 degrees. Find the degree measure of the angle ABD.
The inscribed angle CAD, the degree measure of which is 55, rests on the arc CD, the degree measure of which is twice the angle CAD.
The inscribed CBD angle is also based on the CD arc, therefore, the degree measure of the CBD angle is equal to the degree measure of the CAD angle. Angle CBD = CAD = 55.
Then the angle ABD = (ABC – CBD) = (125 – 55) = 65.
Answer: Angle ABD is 65.
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