WAEC 2017 · Paper 2 · Q2

(a)
Solve the equation $\frac23(3x - 5) - \frac35(2x - 3) = 3$ .
(b)
In the diagram, $P$ , $U$ , $T$ , $S$ lie on a straight line and $P$ , $Q$ , $R$ on another. $\angle STQ = m$ , $\angle TUQ = 80^\circ$ , $\angle UPQ = r$ , $\angle PQU = n$ and $\angle RQT = 88^\circ$ . Find the value of $(m + n)$ .
The values of r, m and n are not given; the drawing uses r = 20°.

Worked solution (try it first)

$\angle TUQ = 80^\circ$ is an exterior angle of $\triangle PUQ$ , so it equals the two opposite interior angles: $r + n = 80^\circ$ (1).
At $T$ , the angle inside $\triangle PQT$ is $180^\circ - m$ (angles on a straight line).
$\angle RQT = 88^\circ$ is an exterior angle of $\triangle PQT$ : $r + (180^\circ - m) = 88^\circ$ , so $m - r = 92^\circ$ (2).
Add (1) and (2): the $r$ terms cancel, giving $m + n = 172^\circ$ .