The quadrilateral ABCD is inscribed in a circle. The ABC angle is 130 degrees, the CAD
| September 15, 2021 | education
The quadrilateral ABCD is inscribed in a circle. The ABC angle is 130 degrees, the CAD angle is 79 degrees. Find the angle ABD.
The inscribed angle CAD = 79 and rests on the arc CD, then the degree measure of the arc CD = 2 * 79 = 158.
The inscribed angle ABC = 130 and rests on the arc ADC, then the degree measure of the arc ADC = 2 * 130 = 260.
Then the degree measure of the arc АD = ᵕADС – ᵕСD = 260 – 158 = 102.
The inscribed angle ABD rests on the arc AD and is equal to half of its degree measure. Angle ABD = 102/2 = 51.
Answer: The angle ABD is 51.
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