WAEC 2024 · Paper 1 · Q45

In the diagram, $TU$ is a tangent to the circle at $P$ . If $\angle PTS = 44^\circ$ and $\angle SQP = 35^\circ$ , find $\angle PST$ .

Worked solution (try it first)

$\angle SPT$ is between the tangent $PT$ and the chord $PS$ , so it equals the angle in the alternate segment: $\angle SPT = \angle SQP = 35^\circ$ .
The angles of triangle $PST$ add up to $180^\circ$ : $\angle PST = 180^\circ - 44^\circ - 35^\circ$
$= 101^\circ$ , option A.