WAEC 2023 · Paper 2 · Q12

(a)
In the diagram, $\overline{PQ} \parallel \overline{MN}$ , $|PR| = |QR|$ , $\angle QMN = 53^\circ$ and $\angle MNP = \left(\frac32 y - 13\right)^\circ$ . Find: (i) $\angle PRQ$ ; (ii) the value of $y$ .
Separate values with commas, e.g. 3, −2
(b)
A bowl contains 15 yellow and green balls of the same size. If the probability of selecting a yellow ball is $\frac25$ , find the number of: (i) yellow balls; (ii) green balls in the bowl.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$PQ \parallel MN$ , and $QM$ crosses both, so the alternate angles are equal: $\angle PQR = \angle QMN = 53^\circ$ .
$|PR| = |QR|$ , so triangle $PQR$ is isosceles and $\angle QPR = \angle PQR = 53^\circ$ .
Then $\angle PRQ = 180^\circ - 53^\circ - 53^\circ$
$= 74^\circ$ .

$PN$ also crosses the parallel lines, so $\angle MNP = \angle QPN = 53^\circ$ (alternate angles).
So $\frac32 y - 13 = 53$ , $\frac32 y = 66$ and $y = 44$ .