WAEC Mathematics 2012 Paper

Concept:Angles on a straight line add up to $180^\circ$, and vertically opposite angles are equal.Explanation:From the diagram, $x$, $y$ and $m$ are adjacent angles on the same straight line.Therefore, $x + y + m = 180^\circ$.The angles $y$ and $n$ are vertically opposite angles, so $y = n$.Replacing $y$ with $n$ in the equation gives $x + n + m = 180^\circ$.This can be rewritten as $x + m + n = 180^\circ$.That is exactly statement iii.The other statements are not confirmed by the given angle relations.Answer:Only statement iii is true. Correct option: C.