WAEC 2015 · Paper 2 · Q8

(a)
Using a ruler and a pair of compasses only, construct: (i) a trapezium $WXYZ$ such that $|WX| = 8\text{ cm}$ , $|XY| = 5.5\text{ cm}$ , $|XZ| = 8.3\text{ cm}$ , $\angle WXY = 60^\circ$ and $WX \parallel ZY$ ; (ii) a rectangle $PQYZ$ where $P$ and $Q$ are on $WX$ .
Model answer
Use only a ruler and a pair of compasses: leave every construction arc visible, because the examiner looks for them. Draw $WX = 8$ cm and construct $60^\circ$ at $X$ ; mark $Y$ with $XY = 5.5$ cm. Through $Y$ draw the line parallel to $WX$ . With centre $X$ and radius $8.3$ cm, cut it at $Z$ , then join $WZ$ . For the rectangle, drop perpendiculars from $Z$ and $Y$ to $WX$ , meeting it at $P$ and $Q$ . Measured: $|QX| \approx 2.8$ cm and $\angle XWZ \approx 76^\circ$ .
(b)
Measure: (i) $|QX|$ ; (ii) $\angle XWZ$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$\angle XWZ \approx 76^\circ$ .
Check: $|QX| = 5.5\cos 60^\circ = 2.75$ cm and the height is $5.5\sin 60^\circ \approx 4.76$ cm.
$Z$ is $\sqrt{8.3^2 - 4.76^2} \approx 6.80$ cm along from $X$ , so $|WP| \approx 1.20$ cm and $\angle XWZ = \tan^{-1}\frac{4.76}{1.20}$
$\approx 76^\circ$ .