WAEC Mathematics 2015 Theory — Question 13
Question 13 of 22 from the West African Examinations Council (WAEC) Mathematics 2015 Theory paper, with the correct answer and a full explanation.
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8(a). Using a ruler and a pair of compasses only, construct: (i) trapezium WXYZ such that |WX|=8cm, |XY|=5.5cm, |XZ|=8.3cm, ∠WXY=60° and WX//ZY; (ii) rectangle PQYZ where P and Q are on line WX. (b) Measure: (i) |QX|; (ii) ∠XWZ.
Model answer
Construction procedure: draw a straight line and mark point W; using compasses, mark X 8cm from W; construct ∠WXY=60° and mark Y 5.5cm from X; construct a line through Y parallel to WX; locate Z on this new line such that |XZ|=8.3cm; join the points to complete trapezium WXYZ. Construct perpendiculars from Y and Z to meet line WX at Q and P respectively, forming rectangle PQYZ. (b)(i) |QX| ≈ 2.7cm (measured from the accurate construction). (ii) ∠XWZ ≈ 76° (measured from the accurate construction).
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