Quadrilateral ABCD is inscribed in a circle. The angle ABC is 138 degrees, the CAD angle is 83 degrees. Find the angle ABD.
| September 17, 2021 | education
In an inscribed quadrangle in a circle, the sum of the opposite angles is 180, then the angle АDC = 180 – 138 = 42. In the triangle АDC, the angle АСD = 180 – 83 – 42 = 55.
Since the angle ACD and ABD are based on the same arc AD, the angle ACD = ABD = 55.
Answer: Angle ABD = 55.
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