BECE Mathematics 2024 Paper

Concept:Draw a line through the vertex of $x$ parallel to $PQ$ and $ST$. Alternate angles between parallel lines are equal, angles on a straight line add up to $180^\circ$, and angles at a point add up to $360^\circ$.Solution:At line $PQ$, the $35^\circ$ angle is vertically opposite the angle between the upper arm and the part of the line towards $Q$, so that angle is also $35^\circ$.By alternate angles, the upper arm makes $35^\circ$ with the dashed parallel line.At line $ST$, the $140^\circ$ angle and the angle between the lower arm and the part towards $T$ lie on a straight line:$180^\circ - 140^\circ = 40^\circ$By alternate angles, the lower arm makes $40^\circ$ with the dashed line.Angle between the two arms (the small angle) $= 35^\circ + 40^\circ = 75^\circ$$x$ is the reflex angle at the vertex, so$x = 360^\circ - 75^\circ = 285^\circ$Key point: The full circle in the diagram marks the reflex angle. $75^\circ$ is the small angle between the arms, not $x$.Answer:Option D ($285^{\circ}$)