WAEC 2018 · Paper 2 · Q4

(a)
A man was charged 2 kobo per month for every ₦1.00 he borrowed from a bank. At what rate per annum was the interest charged?
(b)
In the diagram, $W$ , $X$ , $Y$ , $Z$ are points on a circle with $|WX| = |XY| = |YZ|$ and $\angle WXY = 80^\circ$ . What is the size of $\angle XWZ$ ?

Worked solution (try it first)

$|WX| = |XY|$ , so triangle $WXY$ is isosceles: $\angle XWY = \angle XYW$
$= \frac{180^\circ - 80^\circ}{2}$
$= 50^\circ$ .
Angles in the same segment: $\angle XZY = \angle XWY = 50^\circ$ .
$|XY| = |YZ|$ , so $\angle ZXY = \angle XZY = 50^\circ$ , and $\angle XYZ = 180^\circ - 100^\circ$
$= 80^\circ$ .
$WXYZ$ is a cyclic quadrilateral, so $\angle XWZ = 180^\circ - \angle XYZ$
$= 100^\circ$ .