prove that the sum of the angles in the four exterior segment of a cyclic quadrilateral is equal to 6 right angles
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PQRS is a cyclic quad. and angles ∠A, ∠B, ∠C and ∠D are angles in the four exterior segments. Join AR and AS. In cyclic quad. AQBR, ∠1 + ∠B = 180° In cyclic quad. ARCS, ∠2 + ∠C = 180° In cyclic quad. APDS, ∠3 + ∠D = 180° ∴ ∠1 + ∠2 + ∠3 + ∠B + ∠C + ∠D = 180° + 180° + 180° = 6 rt. ∠s ⇒ ∠A + ∠B + ∠C + ∠D = 6 rt. ∠s.
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