An architect designs a circular window with centre O. Points A, B, C and D lie on the circumference such that ABCD is a cyclic quadrilateral. Angle DAB = 85° and angle BCD = 95°. Which statement must be true?

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Question

An architect designs a circular window with centre O. Points A, B, C and D lie on the circumference such that ABCD is a cyclic quadrilateral. Angle DAB = 85° and angle BCD = 95°. Which statement must be true?

Accepted Answer

Angle ABC + angle CDA = 180° — Award 1 mark for recognising that opposite angles in a cyclic quadrilateral are supplementary. A is incorrect — angle ABC is opposite to angle CDA, not equal to angle BCD. C is incorrect — this would make ABC equal to DAB, which is not a property of cyclic quadrilaterals. D is incorrect — a rectangle would require all angles to be 90°, which contradicts the given information.

Answer

Angle ABC = 95°

Answer

ABCD is a rectangle

Answer

Angle ABC = 85°

Answer

Angle ABC + angle CDA = 180°

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