JAMB 1990 · UME · Q37

Circle geometry

In the figure, $PQRS$ is a circle and $PQT$ and $SRT$ are straight lines. If $\angle SPQ = 81^\circ$ and $\angle PTS = 22^\circ$ , find $x = \angle PQR$ .

Worked solution (try it first)

The angles of triangle $PST$ add up to $180^\circ$ : $\angle PSR = 180^\circ - 81^\circ - 22^\circ$
$= 77^\circ$ .
$PQRS$ is a cyclic quadrilateral, and $\angle PQR$ is opposite $\angle PSR$ .
Opposite angles add up to $180^\circ$ : $x = 180^\circ - 77^\circ = 103^\circ$ , option C.

Report a problem with this question