The opposite angles of a cyclic quadrilateral are supplementary angles, they add to
\(\hat{A}+\hat{C}\) = 180° and \(\hat{B}+\hat{D}\) = 180°
Proof:
Draw radii OA and OC
∠AOC = 2∠B (obtuse)
∠AOC = 2∠D (reflex)
2∠B+ 2∠D=360° angle at a point
∠B + ∠D=180°
∠A + ∠C=360°−(∠B + ∠D)
∠A+ ∠C = 360°−(180°)
∠A + ∠C = 180°
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