JAMB 1994 · UME · Q31

In the diagram, $PTS$ is a tangent to the circle $TQR$ at $T$ , $\angle QRT = 60^\circ$ and $\angle QTR = 50^\circ$ . Calculate $\angle RTS$ .

Worked solution (try it first)

The angles of triangle $QRT$ add up to $180^\circ$ : $\angle RQT = 180^\circ - 60^\circ - 50^\circ$
$= 70^\circ$ .
The angle between tangent $TS$ and chord $TR$ equals the angle in the alternate segment, which is the angle at $Q$ .
So $\angle RTS = \angle RQT = 70^\circ$ , option B.