Explanation:
The object of the exercise seems to be to show that opposite angles of an inscribed quadrialteral are supplementary. The total of arcs in a circle is 360°, so the total of half the arcs in a circle will be 180°.
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arc BCD + arc DB = 360°
∠A = (1/2)(arc BCD)
∠C = (1/2)(arc DB)
∠A + ∠C = (1/2)(arc BCD) + (1/2)(arc DB)
= (1/2)(arc BCD + arc DB)
= (1/2)(360°)
∠A + ∠C = 180°
