Cyclic Quadrilateral

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ABCD is a cyclic quadrilateral. This is a name given to a quadrilateral (4-sided polygon) trapped inside a circle with all 4 of its vertices touching the circumference of the circle. 

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Drag any vertex, A,B,C or D, to change its angle. Take note of the sum of the opposite angles - the blacks and yellows.

What is the sum of angle ABC and angle ADC?
What is the sum of angle BCD and angle BAD?