Given cyclic quadrilateral 𝐴𝐵𝐶𝐷 shown in the diagram, prove that 𝑥 + 𝑦 = 180°
Given quadrilateral 𝐴𝐵𝐶𝐷 with 𝑚∠𝐴+ 𝑚∠𝐶 = 180°, prove that quadrilateral 𝐴𝐵𝐶𝐷 is cyclic; in other words, prove that points 𝐴, 𝐵, 𝐶, and 𝐷 lie on the same circle.
Given a convex quadrilateral, the quadrilateral is cyclic if and only if one pair of opposite angles is supplementary. The area of a triangle with side lengths 𝑎 and 𝑏 and acute included angle with degree measure 𝑤: The area of a cyclic quadrilateral 𝐴𝐵𝐶𝐷 whose diagonals 𝐴𝐶 and 𝐵𝐷 intersect to form an acute or right angle with degree measure 𝑤:
CYCLIC QUADRILATERAL: A quadrilateral inscribed in a circle is called a cyclic quadrilateral.
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