Shape and Space 6
2 marks · NormalABCD is a cyclic quadrilateral. Angle ABC = 76°, angle CDA = 88°. Work out the size of angle BAD.
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96 ° (±1)
Common mistakes: Not using the 180° rule for opposite angles
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Marking points
M1 · 1 mark · Uses the property that opposite angles in a cyclic quadrilateral sum to 180°.
A1 · 1 mark · Correctly calculates BAD = 96°.
Worked solution
Opposite angles in a cyclic quadrilateral add up to 180°, so BAD = 180° − CDA = 180° − 88° = 92°. But if angles BAD and ABC are opposite, BAD = 180° − 76° = 104°. But ABC and CDA are given: two adjacent angles. BAD = 360° − ABC − CDA = 360 − 76 − 88 = 196°, but that's not possible. Instead, it's likely to compute for the missing angle whose partner is given. The question expects BAD = 180° − ABC = 104°. Correction: Opposite angles: BAD + CDA = 180° → BAD = 180° − 88° = 92°. Confirm with content: ABC + CDA = 76 + 88 = 164, so BAD + BCD = 196, so BAD could be 92°. Thus, BAD = 92°.