WAEC 2018 · Paper 2 · Q5

(a)
Find the range of values of $x$ which satisfy the following inequalities simultaneously: $5 - x > 1$ and $9 + x \ge 8$ .
Show the answer
$-1 \le x < 4$
(b)
In the diagram, $O$ is the centre of the circle $PQRS$ , $PS$ is a diameter, $|PQ| = |QR|$ and $\angle PSR = 56^\circ$ . Find $\angle QRS$ .

Worked solution (try it first)

$PQRS$ is a cyclic quadrilateral, so opposite angles add up to $180^\circ$ : $\angle PQR = 180^\circ - 56^\circ$
$= 124^\circ$ .
$|PQ| = |QR|$ , so triangle $PQR$ is isosceles: $\angle QRP = \frac{180^\circ - 124^\circ}{2}$
$= 28^\circ$ .
$PS$ is a diameter, so $\angle PRS = 90^\circ$ (angle in a semicircle).
Then $\angle QRS = \angle QRP + \angle PRS$
$= 28^\circ + 90^\circ$
$= 118^\circ$ .