JAMB 1994 · UME · Q27

In the diagram, $O$ is the centre of the circle and $SOQ$ is a diameter. If $\angle PRS = 38^\circ$ , what is the value of $\angle PSQ$ ?

Worked solution (try it first)

Angles in the same segment are equal.
$\angle PQS$ and $\angle PRS$ both stand on arc $PS$ , so $\angle PQS = 38^\circ$ .
$SQ$ is a diameter, so $\angle SPQ = 90^\circ$ (angle in a semicircle).
The angles of triangle $PSQ$ add up to $180^\circ$ : $\angle PSQ = 180^\circ - 90^\circ - 38^\circ$
$= 52^\circ$ , option D.