WAEC Mathematics 2025 Theory — Question 12

Question 12 of 19 from the West African Examinations Council (WAEC) Mathematics 2025 Theory paper, with the correct answer and a full explanation.

10(b) . In the diagram, A, B, C and D are points on a circle. AB||DC, AC and BD intersect at X and ∠BDC = 40°. Find: (i) ∠ACD (ii) ∠AXD

Model answer

(i) ∠ACD = ∠BDC = 40° (alternate segment / alternate angles, AB∥DC) ∠ACD = ∠CAB = 40° (same segment) (ii) ∠AXD = ∠ACD + ∠CAB = 40° + 40° = 80°

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