BECE Mathematics 2024 Paper

Concept:Use a parallel line to transfer angles and the rule that angles around a point sum to $360^\circ$.Explanation:Draw a third line through the vertex of $x$, parallel to $PQ$ and $ST$.By alternate angles, the angle between the upper arm and this new line is $35^\circ$.On the straight line at $ST$, $140^\circ$ and the adjacent angle $d$ add to $180^\circ$.So $d = 180^\circ - 140^\circ = 40^\circ$.By alternate angles again, the angle between the lower arm and the new line is also $40^\circ$.At the point where the arms meet, the two small angles and the reflex angle $x$ form a full turn.Therefore $35^\circ + 40^\circ + x = 360^\circ$.So $x = 360^\circ - 75^\circ = 285^\circ$.Answer:$x = 285^\circ$, which is Option D.