Mathematics · May / June 2026 · Paper 22 · Question 15
0580
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0580/22/M/J/26 © Cambridge University Press & Assessment 2026 15 75Ě 20Ě A Ā ě Í Ĝ C NOT TO SCALE A, Í, C and Ĝ are points on a circle. Āě is a tangent to the circle at A. Angle AĜÍ ¢ 20° and angle ÍCĜ ¢ 75°. Find angle ĀAĜ. Give a reason for each step of your working. angle ĀAĜ ¢ [5] ĬÑĊ Ġ
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∠EAD = 55 Opposite angles of a cyclic quadrilateral sum to 180 and Alternate segment theorem and no reason linked with inappropriate working [14]
B3 B2 for ∠ABD = 55 Angles may be seen on diagram for B1 or B2.
or B1 for ∠BAD = 105 or ∠BAF = 20 oe e.g. 180 – (105 + 20), 75 – 20 OR
M2 for 180 – (180 – 75) – 20 oe
B2 B1 for opposite angles of a cyclic Allow supplementary and equal/add to for sum to. quadrilateral sum to 180 Allow angles in opposite segments sum to 180. Do not allow just ‘alternate segment’, alternative or Alternate segment theorem segment theorem, AST, alt segment theorem, alternate angles, opposite segment theorem.
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