NECO 2022 · Paper 1 · Q46

In the figure, $PQ$ and $PR$ are tangents from $P$ to a circle with centre $O$ . If $\angle QPR = 34^\circ$ , find the angle marked $x$ .

Worked solution (try it first)

A tangent meets the radius at $90^\circ$ , so $\angle OQP = \angle ORP = 90^\circ$ .
The angles of quadrilateral $OQPR$ add up to $360^\circ$ : $x + 90^\circ + 90^\circ + 34^\circ = 360^\circ$ .
So $x = 360^\circ - 214^\circ = 146^\circ$ , option C.