JAMB 1983 · UME · Q47

In the diagram, $PS = SR$ and $PQ \parallel SR$ ; $\angle PSR = 130^\circ$ and $\angle PRQ = 100^\circ$ . What is the size of $\angle PQR$ ?

Worked solution (try it first)

$PS = SR$ , so triangle $PSR$ is isosceles and its base angles $\angle SPR$ and $\angle SRP$ are equal.
Each is $\frac{180^\circ - 130^\circ}{2} = 25^\circ$ .
$PQ \parallel SR$ , so $\angle RPQ = \angle SRP = 25^\circ$ (alternate angles).
The angles of triangle $PQR$ add up to $180^\circ$ : $\angle PQR = 180^\circ - 25^\circ - 100^\circ$
$= 55^\circ$ , option C.