The quadrilateral ABCD is inscribed in a circle. The ABC angle is 136 °, the CAD angle is 82 °. Find the angle ABD.
| September 4, 2021 | education
The inscribed angle CAD = 82 and rests on the arc CD, then the degree measure of the arc CD = 2 * 82 = 164.
The inscribed angle ABC = 130 and rests on the arc ADC, then the degree measure of the arc ADC = 2 * 136 = 272.
Then the degree measure of the arc АD = ᵕADС – ᵕСD = 272 – 164 = 108.
The inscribed angle ABD rests on the arc AD and is equal to half of its degree measure. Angle ABD = 108/2 = 54.
Answer: The value of the angle ABD is 54.
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