How can you prove that the sum of the angles of a cyclic quadrilateral is 360 degrees using properties of inscribed angles?

To prove that the sum of the angles of a cyclic quadrilateral is 360 degrees using properties of inscribed angles, consider a cyclic quadrilateral ABCD inscribed in a circle. The opposite angles of a cyclic quadrilateral are supplementary, meaning that ∠A + ∠C = 180° and ∠B + ∠D = 180°. Adding these equations gives (∠A + ∠C) + (∠B + ∠D) = 360°. Therefore, the sum of the angles of a cyclic quadrilateral is 360 degrees.

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