A quadrilateral ABCD is inscribed in a circle, find the angle ACD if the angles BAD and ADB are 56 degrees
| March 15, 2021 | education
A quadrilateral ABCD is inscribed in a circle, find the angle ACD if the angles BAD and ADB are 56 degrees and 78 degrees, respectively.
Consider the triangle ABD and determine the value of the angle ABD.
Angle ABD = (180 – BAD – ADB) = (180 – 56 – 78) = 46.
The inscribed angle ABD rests on the arc AD, then the degree measure of the arc AD = 2 * 46 = 72.
The sought, inscribed angle ACD also rests on the arc AD, then the angle ACD = 72/2 = 36.
Answer: Angle ACD = 36.
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