The quadrilateral ABCD is inscribed in a circle. The ABC angle is 110, the CAD angle is 65. Find the ABD angle.

In an inscribed quadrangle in a circle, the sum of the opposite angles is 180, then the angle АDC = 180 – 110 = 70. In the triangle АDC, the angle АСD = 180 – 70 – 65 = 45.

Since the angle ACD and ABD are based on the same arc AD, the angle ACD = ABD = 45.

Answer: Angle ABD = 45.




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